refactor(handler/restack): Move options into requests

[abhinav]

Extracted from #1307

Restack handler entry points now receive operation request structs
instead of loose branch and options parameters. The request structs carry
optional Options fields, matching the handler request pattern used by the
surrounding handler packages.

UpstackOptions embeds the shared Options type while keeping SkipStart as
the only active option. AutoResolve is intentionally not part of this
commit.

[skip changelog]: no user facing changes

[abhinav]

This change is part of the following stack:

• refactor(handler/restack): Move options into requests #1332 ◀

_{Change managed by git-spice.}