Follow up tracking for PR #8754 (Outbound Remote Signer)

[ViktorT-11]

In PR #8754, we introduce a new alternative remote signer implementation called an “Outbound Remote Signer.”

This issue is intended to track any feedback from that PR that we’ve decided is better addressed in follow-up PR(s) rather than in #8754.

Links to the relevant feedback are listed below:

• Add Outbound Remote Signer implementation #8754 (comment)

• Add Outbound Remote Signer implementation #8754 (comment) - Specifically the part about "Sharing the main chain's middleware state"