First of all, like pointed out in the first comment on your question, you're confusing the "witness program" and "witness script". The witness program for p2wpkh is OP_0
followed by the 32-byte SHA-256 hash of the witness script.
So it seems that you are actually asking about the witness script.
To answer your question directly: no, there are no standard witness scripts.
The witness script obviously depend on what you are trying to achieve. The most common use case for p2wsh would be multisig addresses, but they can be used for various other use-cases like policies with time-locked backup spend paths, lightning channel setup, etc.
Each use-case and in fact each application will have to specify the Script they use in the p2wsh policy. There is no real standard among those scripts. However, there are some things to consider:
Whatever Script you are using, you need to remember the script in order to spend the money that is in them. Usually this is something that your wallet will do, but for example if the wallet you are using goes out of service, you will need to know the type of script they use in order to recover your money, alongside the seed phrase.
Many users will use tools like miniscript Script descriptors to turn a script policy into a Bitcoin Script. These users can store the Script descriptor as a backup together with their seed phrase. Script descriptors were introduced exactly to overcome the problem of each wallet having their own scripts.
In several cases, among multisig-enabled wallets that don't support miniscript descriptors yet, the "Script template" they use is either very trivial (a simple multisig f.e., even though f.e. the order of keys also matters here, already making it less trivial), or the template is documented online and a user could potentially find out how to recover their money when they only know their seed phrase.
To conclude, witness scripts used in p2wsh addresses are not standardized and ideally your wallet provider would instruct you to backup a miniscript descriptor alongside the seed phrase so that users can actually recover their coins in the event where the wallet provider disappears and/or the wallet app becomes unusable.