: How to develop an internal intuition for note timings? I have identified three main problems holding back my piano sight reading, and this is the last of them. Although I can play notes with the right timing by very slowly

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Counting while playing is already the way to go! Be patient and don't give up. It will come.

I think what will help you is practicing to identify the big beats in a rhytmically complicated measure. Do it often just with the score, away from the piano. There's no shame in indicating with a small pencil line where every beat falls, for complicated rhythms you can even indicate the smaller subdivisions. When you know how the rhythm is built you can tap it out or sing it while concentrating on feeling the underlying beat. When you can do that, it's time to do it at the piano

Ofcourse while sightreading you can't take out your pencil to write on your score but if you do this regularly it becomes second nature and you will be able to 'see' these beats and their subdivisions instantly, when you see a complicated bar.

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The There are time inducations as andante, adagio etc. and even beats/min. advices.

So you can look up how many beats/min. an allegro ma no troppo would be and count the bars you have to play per minute.

But your problem seems to be a quite different one. All the time indications concerning the speed of music piece are only propositions to me. Sometimes I missuse a piece as a technical practice and play it in double
speed. Or even in performance I conduct it very slowly not to make angry the band members or the congregation, but the feed back can be complaining.

Some piano music I will never be able to play in the “correct” speed but I don’t mind at all. My goal is not to become perfect or be an virtuous but I would like to enjoy as many compositions as possible and improve my technic, my understanding of harmony and sight reading. I will be able to accompany a group or an ensemble or myself when singing and I know I will never be perfect. Perhaps this will help you to consider and reflect your own playing.

So if you are asking about this understanding of time - just compare different performances and listen to the different duration by different interpretations.

But if your problem is concerning the time signature and the rhythm you have to look up this SE site under sight reading and rhythm as there are already many answers and advices.

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Try to start recognising common groupings of rhythmic values as patterns in their own right. This is a bit like moving away from reading one letter at a time when learning English to being able to recognise a whole word almost instantaneously in a single operation.

The way that halving a note value is often just a question of adding another beam or flag means that a crotchet followed by two quavers can be recognised as having the same duration relationships as a quaver followed by two semiquavers - so the patterns you learn can translate to longer and shorter levels of note duration.

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Practice a variety of two part rhythms.

use a metronome
count out load while practicing (video on the psychology of counting out loud)
use a good counting system (rhythm syllables like Kodaly) to develop awareness of the beat versus subdivisions
pay attention to both composite rhythms and the individual rhtyhms, make sure the accents in each individual rhythm is correct

There are a lot of rhythm practice books available, or you could make your own exercises.
I didn't like the books I was finding - the rhythms seemed too irregular - so I made my own cards for simple & compound meters with also syncopation and polyrhythms. I made sure the counting syllables were clear...

...if you can't find a published resource for your needs, make your own.

A general though about sight reading:

I mostly play classical/romantic music like Chopin, Rachmaninoff, Debussy, Liszt, and Scriabin...
I've listened to it many times while reading the music so I know exactly what it should sound like

It sounds like you are reading that 19th century repertoire, but not sight-reading it. That's fine, but it's really two different kinds of reading.
I don't know that you have only difficult material from those composers, but I suspect that may be the case.
You want to make sure you are sight reading the right level of music. With that 19th century repertoire a lot was not meant for sight reading but virtuosic display.

for 19th century style try finding simpler, shorter stuff like Schumann's Album for the Young, Schubert's keyboard dances, Burgmuller op.100, piano accompaniment parts from song albums might offer good material too. But dances sets and collections for young/beginners are a good place to start looking.
18th century classical style, Czerny is a great source. Lot of people dump on Czerny, but look at the Recreations, Progressive Studies, etc they offer lots of charming, modest pieces. Also typical keyboard instruction manuals from this time follow a format of music fundamentals and basic fingerings followed by a collection of fairly easy pieces. Clementi's Art of Piano Forte Playing is a good example. Also, get L. Mozart's Nannerl Notebook and W.A. Mozart's London Sketchbook. Those are filled with tons of short pieces.
18th century baroque style, get the Bach notebooks for Wilhelm Friedman and Anna Magdalena. Also, the Bach 371 Harmonized Chorales for keyboard are sight readable. There are endless dance suites and dance sets in this period. Telemann's 36 Keyboard Fantasias, Handel's sonatinas, and other small scale early sonata forms could be good sight reading material too.

A huge amount of the material above is available at imslp.org. You probably can see there is a theme of dance forms. The important thing about that genre is much of it was meant for amateur players and home entertainment. Most of it wasn't virtuosic concert material. I think a lot of it was meant to be read and played without a huge amount of preparation. That kind of stuff should make good sight reading material.
Volume is important. Get enough material that you can't memorize it.

Simpler music isn't really much fun, that's why. And I have succeeded at learning many such pieces despite my limitations

This may be an impasse. If you enjoy the technical challenge of difficult music, then sight reading doesn't seem like a type of playing to satisfy you. "To each his own" I suppose. You don't have to sight read if you don't like to do it.
But I think you want to make a clear distinction what sight reading is about. I'm curious to see if anyone disagrees with me, but people don't sight read stuff like Debussy's Preludes or Liszt's Etudes. Sight reading is for smaller scale stuff of modest difficulty not virtuosic display.