Improvements enabled by new wat parser

[tlively]

This is an umbrella tracking issue for further improvements enabled by the new wat parser work. (The parser work itself was tracked in #6208.)

• #6612
• #6613
• #6614
  • #6407
• #6615
• #6616

[laptou]

I think #6407 should be included here too, right?

[tlively]

Yes, that was reachable indirectly via #6614, but I've added it explicitly above.