（WIP)*(ticdc): remove cdc context

[sdojjy]

What problem does this PR solve?

Issue Number: close #xxx

What is changed and how it works?

Check List

Tests

• Unit test
• Integration test
• Manual test (add detailed scripts or steps below)
• No code

Questions

Will it cause performance regression or break compatibility?

Do you need to update user documentation, design documentation or monitoring documentation?

Release note

Please refer to [Release Notes Language Style Guide](https://pingcap.github.io/tidb-dev-guide/contribute-to-tidb/release-notes-style-guide.html) to write a quality release note.

If you don't think this PR needs a release note then fill it with `None`.

[asddongmen]

Please also change the package name from context to another more proper name.

[zhangjinpeng87]

@sdojjy Please describe in the PR what problem you are trying to solve, and how do you solve it.

[sdojjy]

/retest-required

[ti-chi-bot[bot]]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: 3AceShowHand, asddongmen

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[ti-chi-bot[bot]]

[LGTM Timeline notifier]

Timeline:

• 2024-04-03 07:07:51.95260432 +0000 UTC m=+427733.480144870: :ballot_box_with_check: agreed by 3AceShowHand.
• 2024-04-03 07:11:08.248133067 +0000 UTC m=+427929.775673613: :ballot_box_with_check: agreed by asddongmen.

[codecov[bot]]

Codecov Report

Merging #10279 (ef48a12) into master (c022fe0) will decrease coverage by 0.0032%. Report is 1 commits behind head on master. The diff coverage is 56.9230%.

Additional details and impacted files

Components	Coverage Δ
cdc	61.6639% <56.9230%> (-0.0158%)	:arrow_down:
dm	51.2677% <ø> (+0.0161%)	:arrow_up:
engine	63.4161% <ø> (+0.0070%)	:arrow_up:

Flag	Coverage Δ
unit	57.3943% <56.9230%> (-0.0032%)	:arrow_down:

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

@@               Coverage Diff                @@
##             master     #10279        +/-   ##
================================================
- Coverage   57.3974%   57.3943%   -0.0032%     
================================================
  Files           850        849         -1     
  Lines        125070     124988        -82     
================================================
- Hits          71787      71736        -51     
+ Misses        47897      47861        -36     
- Partials       5386       5391         +5