fix: replace bad simp lemmas for Id

[eric-wieser]

This PR reworks the simp set around the Id monad.

In particular, it stops encoding the "defeq abuse" of Id X = X in the statements of theorems, instead using Id.run and pure to pass back and forth between these two spellings.

This fixes the problem with the current simp set where Id.run (pure x) is simplified to Id.run x, instead of the desirable x.
This is particularly bad because the x is sometimes inferred with type Id X instead of X, which prevents other simp lemmas about X from firing.

Making Id reducible instead is not an option, as then the Monad instances would have nothing to key on.

[eric-wieser]

changelog-library

[eric-wieser]

I've split some helper lemmas to #7356, which are independent of this fix

[leanprover-community-bot]

Mathlib CI status (docs):

• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase 9ae2ac39c9512461643e268f0feff5654044776f --onto 5536281238dff2fb4e0a54da472d4f0d6496069e. You can force Mathlib CI using the force-mathlib-ci label. (2025-03-06 03:18:31)
• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase e0fa6a1792458af81c8f421f5e75bfbc4117f617 --onto 7bfa8f6296ebfebc497d5b30d34f494bcc9782a2. You can force Mathlib CI using the force-mathlib-ci label. (2025-03-10 23:19:19)
• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase e0fa6a1792458af81c8f421f5e75bfbc4117f617 --onto 8fc8e8ed19ef218022f5a94cbf5e472e3b777e44. You can force Mathlib CI using the force-mathlib-ci label. (2025-03-11 23:53:26)
• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase d538e1cd90bc8dce3e8919d2ed496903577a63a9 --onto c1d145e9d70569274ac868805b4a8591d09718af. You can force Mathlib CI using the force-mathlib-ci label. (2025-03-14 01:21:44)
• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase 5c333d88c01f71180f1ceeb00fcdad2bea1bdbf9 --onto c1d145e9d70569274ac868805b4a8591d09718af. You can force Mathlib CI using the force-mathlib-ci label. (2025-03-14 01:50:23)