Based on my knowledge, you need to install .Net Framework 4.8 or 4.7.2 to support the Exchange 2013 CU23.
And note that only .Net Framework 4.8 could support Exchange 2019 CU9.
should i upgrade current forest\ domain function levels or it gonna work.
You should raise the forest function level to Windows Server 2012 R2 to support Exchange 2019.
for exchange 2019 cu9, what IE or chrome version should i use (install or update to latest version)
You can use the latest version Microsoft Edge, and you can check other browsers in these articles.
Browsers that support OWA : Web browsers supported for use with the premium version of Outlook Web App or Outlook on the web
And browsers that support EAC: Exchange Admin Center Supported browsers
Note that Exchange 2019 Mailbox/Edge Transport roles could only be installed on Windows server 2019.
I think this article would be helpful: Exchange Server 2019 system requirements, Exchange Server supportability matrix.
And Exchange Deployment Assistant could help you in upgrading.
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