[roll recipes_version.txt] checkout: Remove unused code from CheckoutApi

Remove unused code (or code that should be unused) from CheckoutApi.
Some of it gets added to CheckoutContext, some just gets deleted. Update
callers to use new locations.

Original-Bug: 600
Original-Reviewed-on: https://pigweed-review.googlesource.com/c/infra/recipes/+/82940

https://pigweed.googlesource.com/infra/recipes
recipes_version.txt Rolled-Commits: af64d3eb0268e71..e918fc8b2da4fae

GitOrigin-RevId: cc8cfe1d8352183e9629229146cfd4c8b52935b1
Change-Id: I4872a25bedac936bd5b9421ea5cb43420399397a
diff --git a/recipes_version.txt b/recipes_version.txt
index a1e856f..5f8a7bb 100644
--- a/recipes_version.txt
+++ b/recipes_version.txt
@@ -1 +1 @@
-af64d3eb0268e7120880bb5e8618b22e26372ea7
\ No newline at end of file
+e918fc8b2da4faecf0645c05b2aed0d4500b6da5
\ No newline at end of file