SESSIONS-3933: Refine function name [PATCH-2]

[BohuTANG]

I hereby agree to the terms of the CLA available at: https://databend.rs/dev/policies/cla/

Summary

Summary about this PR:

1. Rename *MgrApi to *Api in management
2. Rename context_shared to query_context_shared

Changelog

• Improvement

Related Issues

PATCH-2 of #3933

Test Plan

Unit Tests

Stateless Tests

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[zhang2014]

Look good to me.

[PsiACE]

LGTM

[codecov-commenter]

Codecov Report

Merging #4021 (a9872b3) into main (ffd5026) will increase coverage by 0%.
The diff coverage is 57%.

@@          Coverage Diff          @@
##            main   #4021   +/-   ##
=====================================
  Coverage     57%     57%           
=====================================
  Files        817     817           
  Lines      43406   43402    -4     
=====================================
- Hits       24787   24786    -1     
+ Misses     18619   18616    -3     

Impacted Files	Coverage Δ
common/management/src/role/role_mgr.rs	77% <ø> (ø)
common/management/src/stage/stage_mgr.rs	94% <ø> (ø)
common/management/src/udf/udf_mgr.rs	88% <ø> (ø)
common/management/src/user/user_mgr.rs	94% <ø> (ø)
query/src/users/user_api.rs	77% <57%> (+5%)	⬆️
common/containers/src/pool.rs	79% <0%> (+2%)	⬆️

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