Use Lexical HTML serialization

[GermanJablo]

Link to reproduction

No response

Environment Info

Payload: beta.112

Describe the Bug

Lexical to HTML serializer in Payload is custom, and we're not using the official Lexical one ($generateHtmlFromNodes and $generateNodesFromDOM). This increases the scope of what we have to maintain.

The goal is to see if we can migrate to $generateHtmlFromNodes and $generateNodesFromDOM without breaking changes.

This would allow us to incorporate this PR that comes in the next release of Lexical: facebook/lexical#6693 (comment)
and which is one of our most requested issues: 90990.

NOTE: Perhaps this undocumented API can be useful: facebook/lexical#4254

Reproduction Steps

Adapters and Plugins

No response

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