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Let's say you are playing Bach on a classical guitar, which theory concepts do you constantly think of and use? Do you always know the key and the scale you are in? The mode maybe? The interval between each consecutive note or the role of every note in that scale? Do you know if you are building tension or resolving?

I know that for example most of the time, things like rhythm and timing is automatic, and you don't think about it but still, would you be able to know in which beat every note goes while playing?

Let me expand on where my curiosity comes from:

I've been playing guitar for years before starting to take lessons 3 months ago. So my usual way of playing a song consists in learning the chords, memorizing some fillers or the solo without even knowing which key I'm in, then repeat repeat repeat. All from tabs or by ear. 99% memory, 1% theory.

But I've always been aware that to really improve I had to start learning some theory. It's ok, I love everything about music theory and I'm more and more passionate about it but when I try to apply what I'm learning to my playing, it slows me, it takes me like 30 seconds to guess the chord I'm playing if I don't know it, maybe because I try to think about everything before even mastering basics like the notes on the fretboard.

I can answer about Bach on piano, but I think the ideas should apply on guitar.

In a lot of Bach's music imitative counterpoint is important. When the musical subject gets stated and re-stated in imitation as the music progresses I'm aware of those entries and I use that understanding to articulate the music and bring out the subject. The articulation could take many forms, but that isn't important as far as your question is concerned. The important thing is having the theoretical understanding of the music to recognize the subject and its imitation and then exploiting it to shape the performance.

Another very important application of theory would be identifying cadences or temporary key changes and using that to execute good phrasing. Again the exact execution could be handled many different ways - perhaps a little ritard is applied at cadences to articulate the phrase endings - the important thing is the theoretical knowledge about cadences and phrasing needed to understand the music structure and using that to render a good performance.

I also pay attention to scale degrees and the counterpoint interaction of bass and melody at important harmonic points. For example, if a V7 resolves to I I pay attention to the FA to MI (^4 to ^3) resolution. If a tonic chord is in first inversion I6 to pay attention to which chord tone is in the melody. Maybe I don't do anything with this performance-wise, but I stay aware of these important harmonic tones. Probably it is a memory aid as it focuses on the essential musical framework.

Those would be some examples of a direct linking of theory to a good performance. Other things may come up that don't seem as essential and don't receive much conscious thought. Like a harmonic sequence. I notice the sequence. That's structurally important. But maybe I don't dwell on the exact chord names of each sequenced event. I care more about where it ends in terms of key.

Don't mistake that for indifference or not analyzing the music at all. Generally, I try analyzing everything I play with Roman numerals (unless such analysis doesn't make sense of the harmonic style.) But while actually playing I don't necessarily think about every single chord name.

One other theory thing I do all the time is look for real examples of music that breaks so-called theory rules! I think some people make too big a deal about rules so I like having examples to the contrary. I circle and write details such examples in my scores.

How much theory...?

I'm not sure how you would quantify it. But you probably aren't literally asking 'how much' for a quantity. I imagine it's more about what theory and why it matters in performance.

Theory is not a hammer. It's more like an Encyclopedia of Hammers. So it wouldn't be super handy to have it open just in case while hitting some nails. It might get in a way - we might look into it and hit a finger instead of nail.

But then, in the evening, there might be a time for a reflection. Was I using the right hammer today? Maybe the hammer from page 56 was much better tool for the job?

So while not really useful on the job, the Encyclopedia of Hammers might help in a long term to integrate the way we think about hammers, make us choose better hammers and very often prevent us from using hammers to smash already open doors.

Anyway, thinking while playing, and by thinking I mean some conscious decision making based on theory, simply should never happen. Performance is a different realm where "thinking" gets in the way of more meditative type of focus and physical connection to the instrument.

(Another answer from piano background.)

Theory is vital for good sight reading. Instead of seeing a pagefull of individual notes, you can see groups of patterns. You can look at the shape of the notes and the context and see "oh, that just outlines a V7 chord, then that next one is probably I," and then you just have to read two patterns instead of 7+ notes and then you're free to worry about other stuff instead.

(Not that I can just recognize every chord on sight, but things like I and V tend to stick out.)

If you don't know theory, maybe something has a lot of "random" accidentals you have to keep track of (especially if it's minor)! But if you understand how that extra sharp comes from modulating to a new key for a bit, or why composers like to use a #7 in minor keys, that's not really something you have to keep track of anymore; it's just a reminder of what you're already expecting.

I'm a student of music theory and I find it quite interesting, but when I'm performing and improvising, I'm not consciously thinking about theory. For me the theory comes into play when I'm studying the music away from the stage, kind of like trying to figure out how to improve the way a piece works, before I want anyone to see my performance of it. Theory study offers guidelines / options that I can use to help make a piece of music my own. It occurs to me that any musician that can successfully perform a piece of music, may not realize it, but they do on some level know some music theory and are using it without thinking when they perform the music. That's how I use it.

Just my two cents. Theory will help you understand the music better and maybe get more insight into the composer's intent which might help you interpret it more clearly. It sounds like you do fine the way you do it now, which is playing the music with a minimum of knowing the theory behind it's construction. After playing for years it might be satisfying to reach a deeper level of understanding why the music is put together the way it is. Or not. If you want to write your own then you should learn at least the basics.