Is the ‘t’ in ‘witch’ considered a silent t?

There's no rigorous or official definition of what a "silent letter" is.

The sound represented by the letters "tch" in "witch" is what linguists call an affricate. These are phonetically complex sounds that start with a period of occlusion, which is then "released" with a burst of air and followed by a period of noisy turbulence (frication).

By convention, the International Phonetic Alphabet represents affricates with a sequence of two symbols: the first represents the occlusion, and the second represents the frication. Hence the transcription [tʃ]. But in terms of phonology (the organization of sounds into meaningful units of speech), affricates don't necessarily behave like a sequence of two separate sounds. For example, English words can end in [tʃ], but can't end in sequences of another stop followed by [ʃ], such as [pʃ] or [kʃ] (setting aside marginal cases like loaned proper names). So phonologists generally consider [tʃ] in English to be its own sound (phoneme), not a sequence of the /t/ and /ʃ/ phonemes.

Other systems of phonetic transcription, such as the so-called "Americanist" system, transcribe affricates with single letters, such as [č]. In the International Phonetic Alphabet, affricates can be distinguished from sequences of two separate consonants by using a tie bar (like [t͡ʃ]), although this is often omitted.

The fact that [t͡ʃ] kind of behaves like its own sound is consistent with the fact that it is frequently spelled as "ch", rather than as something like "tsh".

And as you mentioned, since "ch" by itself can represent [t͡ʃ], it's possible to argue that "t" is "silent" in "witch". A competing analysis would be that "tch" is a trigraph where all three letters function together to represent the single sound [t͡ʃ]. In the first analysis, "t" is a silent letter. In the second analysis, it isn't. I know of no compelling evidence that proves which of these alternative analyses is correct.

Even so-called "silent" E can be analyzed in different ways. The word "rate" is pronounced differently from the word "rat", so the "e" in the first can be analyzed as part of a non-continuous digraph "a_e" rather than as an entirely silent letter. In general, it isn't clear whether "silent" means "redundant (could be removed without changing the pronunciation of the letter)", or "has no obvious correspondence to a single phoneme in the word", or "has no obvious correspondence to a single phonetic portion of the word", or some complex combination of some of these. Letters don't actually correspond very well to pronunciation, especially in English. Some letters are conventionally called "silent" as a means of explaining their non-intuitive behavior, but this is more of a pedagogical technique than a fully defined concept. You could say that "i" in "birch" is a "silent letter", since some people pronounce this word with a syllabic R sound and no phonetic vowel (and the spelling "brch" could conceivably represent the pronunciation equally well), but I've never seen people say that.

Perhaps a comedy answer but honestly, I’ve always thought that “which” has a missing “t” whereas “witch” is perfectly sensible as written. Nothing silent there. In my view , it’s the ones WITHOUT the “t” that are the oddities !

Though people from the English town of Norwich may disagree. 😉 (They have silent w issues to address though)

Apart from the fact that a few Americans still aspirate the /h/ in which (long gone in BrE), the full Oxford English Dictionary gives exactly the same pronunciations for both witch and which...

which British English /wɪtʃ/
witch British English /wɪtʃ/

which U.S. English /(h)wɪtʃ/
witch U.S. English /wɪtʃ/

So, yes - the /t/ is always enunciated, even if it's not in the orthography.

Some people pronounce "witch" the same as "which", that is, making the "t" silent. Others pronounce the "t", "witch".

Your examples of words where "ch" makes a "tch" sound puzzle me. I and peole I speak to don't pronounce any of these words with a "t" sound. We don't say "ap-prōtch", we say "ap-prōch". But ignoring that, even if these words were pronounced with a "tch" sound, I agree with you that that would not make it valid to say that the "t" in "witch" is silent. It just means that there is more than one way to express the same sound in English -- hardly a novel insight.

According to LPD (Longman Pronunciation Dictionary, 2008) the trigraph "tch" is regularly pronounced /tʃ/; this means that "tch" is not considered as t followed by "ch", and therefore there is no question about a silent t.

LPD, p. 116 (spelling-to-sound)

Answer to comment from user 76987:

"I’m very confused. I never said anything about whether it’s a matter of convention, and I never asked about why any convention was chosen. I honestly don’t know whether you’re arguing that ‘witch’ does or doesn’t have a silent t."

I am not arguing in the absolute, and that is so because there is no recognizable absolute (perhaps no reseach has been done or if some research has been done it yielded nothing, and in any case there is no result available in non specialized literature). I am arguing that according to a widely accepted convention, there is no logic that makes sensible a question about t being silent or not in words like "witch". At some point in time in the past, linguists have decided to try to see what kind of principles could be found in the pronunciation; that is an endeavour that does not date from very far back in time, it started in the US probably with the efforts of Noah Webster to standardize the pronunciation in the 1780's or so (Noah Webster's standardization of sound). In those days, these early scientists, or perhaps a little later other inquiring minds, were first confronted with words such as "witch" and "which", and they found only one pronunciation for "tch" and "ch". They had a choice to make; whether it was on the basis of historical fact or not (you do not have in all cases historical facts that will allow you to make the most judicious choice), someone decided that a good approach was to consider that there was two consonant clusters and a single sound, and that it was only needed to consider that this single sound was that of the two clusters. There was the other possibility of considering that t was silent in "tch", and obviously not many people chose that path. Today, people who ask about this t being silent are no professionals of the English language although there are those who understand this matter to a certain extent (see the first answer to the question "why is t silent?" in the Quora site).

This decision, to say that t is not silent but that instead in the cluster "tch" t has no incidence of its own (to the contrary of t in "often") and is just part of a group of letters that takes on an "assigned" pronunciation, is essentially a convention (a useful one in my opinion).

In the same vein, why do you accept that there should be the sound of t in "ch" (since there is no letter t in "ch") and why is c silent? C has no incidence of its own in most occurrences of the combination "ch", which as a digraph is considered to have regularly the pronunciation /tʃ/; it is not silent and it is just part of the digraph "ch". In the same way that you can accept that there is the sound /t/ in "ch" you can accept that the sound /tʃ/ is in "tch".

I hope this clears any misunderstanding you might have had, but if there remains blurred ideas in your mind do not hesitate to ask again (but try to be very specific, although there is no certitude that I'll have anything useful to say).