[llvm] [workflows] Avoid usage of access token in issue-write.yml (PR #94011)

[Alexey Bader via llvm-commits]

bader wrote:

> Is there additional context for why this change is needed? I remember seeing something, but can't find it now.

This discussion has the context for this change - https://github.com/llvm/llvm-project/pull/80495#discussion_r1621256638.

https://github.com/llvm/llvm-project/pull/94011