[2.3.x backport] release: integrate manifests into the release process

[jrockway]

No description provided.

[codecov]

Codecov Report

Merging #8040 (aacb79a) into 2.3.x (69f403d) will decrease coverage by 18.79%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##            2.3.x   #8040       +/-   ##
==========================================
- Coverage   22.25%   3.45%   -18.80%     
==========================================
  Files         415     201      -214     
  Lines      112166   74136    -38030     
==========================================
- Hits        24962    2562    -22400     
+ Misses      82919   71213    -11706     
+ Partials     4285     361     -3924     

Impacted Files	Coverage Δ
src/server/auth/db.go	0.00% <0.00%> (-100.00%)	⬇️
src/internal/watch/op.go	0.00% <0.00%> (-100.00%)	⬇️
src/internal/miscutil/log.go	0.00% <0.00%> (-100.00%)	⬇️
src/internal/miscutil/math.go	0.00% <0.00%> (-100.00%)	⬇️
src/internal/grpcutil/error.go	0.00% <0.00%> (-100.00%)	⬇️
src/internal/randutil/unique.go	0.00% <0.00%> (-100.00%)	⬇️
src/internal/testutil/naming.go	0.00% <0.00%> (-100.00%)	⬇️
src/internal/storage/fileset/metadata_store.go	0.00% <0.00%> (-100.00%)	⬇️
src/internal/storage/track/tracker.go	3.70% <0.00%> (-96.30%)	⬇️
src/internal/task/etcd_queue.go	0.00% <0.00%> (-93.55%)	⬇️
... and 362 more

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