tests: Implement LargePut requests

[serathius]

Part of #15102

cc @ahrtr @ptabor

[codecov-commenter]

Codecov Report

Merging #15180 (ef0bdbe) into main (91ec368) will decrease coverage by 0.04%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##             main   #15180      +/-   ##
==========================================
- Coverage   74.54%   74.50%   -0.04%     
==========================================
  Files         415      415              
  Lines       34318    34318              
==========================================
- Hits        25583    25570      -13     
- Misses       7090     7105      +15     
+ Partials     1645     1643       -2     

Flag	Coverage Δ
all	74.50% <ø> (-0.04%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
server/proxy/grpcproxy/watch.go	92.48% <0.00%> (-4.05%)	⬇️
client/v3/leasing/util.go	88.33% <0.00%> (-3.34%)	⬇️
server/etcdserver/api/v3rpc/interceptor.go	73.43% <0.00%> (-3.13%)	⬇️
server/etcdserver/api/v3rpc/watch.go	82.85% <0.00%> (-1.91%)	⬇️
server/etcdserver/api/rafthttp/msgappv2_codec.go	69.56% <0.00%> (-1.74%)	⬇️
pkg/adt/interval_tree.go	85.96% <0.00%> (-1.26%)	⬇️
server/etcdserver/server.go	84.94% <0.00%> (-0.31%)	⬇️
client/v3/watch.go	93.06% <0.00%> (+0.38%)	⬆️
server/etcdserver/v3_server.go	77.66% <0.00%> (+0.69%)	⬆️
server/lease/leasehttp/http.go	65.69% <0.00%> (+1.45%)	⬆️
... and 5 more

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