Are the characters used in syntax of most programming languages dependent on the keys of the standard keyboard or was the standard keyboard made specifically to allow programming with these keys?

Pretty much all programming languages in use today have been invented decades after the keyboard.

The keyboard was originally invented for typewriters, but since they don't interact with anything and are self-contained systems, typewriters don't need their keys standardized. However, the keyboard converged as HP, Brother et al. brought the typewriter forward, especially near the end when typewriters were keyboards connected to printers.

Early computers weren't programmed with keyboards at all and used punch cards to be programmed. As you move forwards with the invention of the computer as we know it today, you find out that the modern keyboard was invented to be able to type most characters in use at the time (a classic example is that the @ sign was used by tellers on tills, to mark stuff like 2 units @ $5 per), and actual standards body such as iso and ANSI simply implemented that.

Early personal computers were not powerful enough to compile programs quickly(and compilers were very expensive), so for a while all programming was done either in assembly, which requires very few special characters, or in higher lever languages by people who could pay to get their programs compiled. These higher lever languages, such as B (precursor to C), were often written right on paper by hand, or by typewriter. After this point, home compilers became more and more accessible (the internet basically guaranteed you could get a compiler if needed), and this was the last point in history you could design a language with characters not present on a standard keyboard (you could still have a nonstandard typewriter, or write them by hand for example). After this and the explosion of home computing, people designed their own languages that they were able to use themselves, using their own keyboards.

Worth noting that there exist languages today that you cannot type, pretty much at all. They are however largely considered esolangs (esoteric languages) and most of their use is relegated to the practice of code-golf, in which a programmer tries to accomplish a task using the fewest bytes. Since the characters on a keyboard make up a fraction of all characters available in Unicode or even just ASCII, these languages try to increase the number of things you can do with a single characters by disregarding the fact you can't type most of them, lowering the amount of bytes one needs to do a task.

An example of this is O5AB1E (pronounced "osable"), which has over 250 single-character commands, such as Δ which "repeats code until 'a' doesn't change".

An example (that you can't type) is: yā<ã.Δ¹sŸèOQ

This program gets an input n and a string of numbers, then outputs the first run in the string that sums to n. The program is explained here