Two big-picture things before I get into a detailed review.

I don't like the idea of storing the options as an attribute on RBClient when the client isn't actually using it at all. I also can't see where web-based auth is implemented for commands other than rbt login.
Architecturally, how does this sound:

Update auth_callback to return a dict instead of a tuple[str, str]. This dict can include either username/password or an API token (actually, probably either dict or tuple and trigger a DeprecationWarning if the caller receives a tuple back).
Update ReviewBoardHTTPPasswordMgr to also plumb that through.
Update ReviewBoardServer.retry_http_basic_auth to handle an API token result.
Add the web-login implementation to BaseCommand.credentials_prompt. This has access to self.options directly.

I think -o is still very important here, and we should keep it for the long term. rbt post -o is a lot easier to type than rbt post --open-browser

Perhaps we should use a dataclass here instead of a dict?

This should be RBClientWebLoginOptions | None

This should use (RBClientWebLoginOptions | None) = None

Type here is incorrect.

I have an idea here. Right now, this will make it so help output will show two separate lines each of these.
How about, instead of duplicating the options, we do:

def create_parser(
    self,
    config: RBToolsConfig,
    argv: (list[str] | None) = None,
) -> argparse.ArgumentParser:
    for option in self._global_options:
        if option.opts[0] == '--open-browser':
            option.opts = ['-o', '--open', '--open-browser']
        elif option.opts[0] == '--web-login':
            option.opts = ['-w', '--web', '--web-login']

    return super.create_parser(config, argv)


That'll simplify the RBClientWebLoginOptions creation too.

Can we add something that triggers a deprecation warning if this option is used?

Can you add docs for the return value and CommandError raise?

This is no longer true.

We could do the same thing here modifying self._global_options instead of duplicating the option.

These should use | None syntax

This should fit on one line.

This should be able to go in the if TYPE_CHECKING block.

This should be able to go in the if TYPE_CHECKING block.

Ship It!

Let's go with 5.4 for this release, since we're introducing new abilities.
This will apply to other version references.

Blank line between the class docstring and attributes.

Can we alphabetize these?

Both of these need their own Version Changed.

I think this will end up polluting the shared options. We'd have to make a copy.
Also, do we want to break after we find the option?

Same note here as with the other location.

Ship It!

Each one of these needs its own Version Changed.

I think this probably should be a Sequence, unless we're allowing manipulation of it. This may become a larger change though, I'm not sure. If so, don't worry about this.

Same note here with Sequence, if going this route for this change.