Fixes #5952 Prevent adding not public CPT posts to cache table

[Khadreal]

Description

Fixes #5952

Documentation

Added a check for post type before adding it to wpr_cache_table

User documentation

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Technical documentation

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Type of change

• Bug fix (non-breaking change which fixes an issue).

New dependencies

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Risks

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Checklists

Code style

• I wrote self-explanatory code about what it does.
• I named variables and functions explicitely.
• I did not introduce unecessary complexity.

[codacy-production]

Coverage summary from Codacy

See diff coverage on Codacy

Coverage variation	Diff coverage
Report missing for d0d3ce01	✅ 100.00% (target: 50.00%)

Coverage variation details

	Coverable lines	Covered lines	Coverage
Common ancestor commit (d0d3ce0)	Report Missing	Report Missing	Report Missing
Head commit (a302839)	37290	14481	38.83%

Coverage variation is the difference between the coverage for the head and common ancestor commits of the pull request branch: <coverage of head commit> - <coverage of common ancestor commit>

Diff coverage details

	Coverable lines	Covered lines	Diff coverage
Pull request (#6722)	2	2	100.00%

Diff coverage is the percentage of lines that are covered by tests out of the coverable lines that the pull request added or modified: <covered lines added or modified>/<coverable lines added or modified> * 100%

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Footnotes

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[MathieuLamiot]

We would need tests on the new bail-out.
Also, I asked on the issue if excluding private post types is expected or not. -> OK on this.

Ok for me now. I'll let the team review.

[MathieuLamiot]

I reproduced the issue on my E2E website with develop, and not with this PR.
I get the same number of preload entries on this PR than on develop without code snippets, no errors and all are preloaded.