Add mod support to replay mode

[Itms]

Currently, only the public mod is loaded when launching the replay mode, and supporting the mods in that mode would make debug easier:

• for modders.
• when adding features to the engine that have an effect on moddability.

There is already a TODO in the code requesting that feature.

[leper]

This shares some code with my modmod work, and I've been planning to do that once I've cleaned that up a bit.

[leper]

In 15676:

Add engine support to load mods from config and restart into mods.

Restructure mod mounting code a bit to make it reusable, and use it for replays. Fixes #2703.