I found this line in my debug.log file:

[Client thread/WARN] [Had Enough Items]: Sending runtime to plugin: thelm.packagedauto.integration.jei.PackagedAutoJEIPlugin took 6768 ms

Seems like its something wrong since usually plugins took less that 50ms to process.

debug.log

Found another place where it listed. There its took about 1% of whole modpack load time.

https://spark.lucko.me/1gJaCkUPrm?hl=330597

You might want to try reporting this issue to Had Enough Items

Hmm, probably its actually HEI config issue.
I rolled back Packaged Auto and found that old versions have same several seconds lag https://spark.lucko.me/umI6BGghcl?hl=355881

This is probably related to HEI config ultraLowMemoryUsage. I will make more tests later.

But, if HEI is culprit here, who other mods that have HEI integration not stalled similar way? I have about 100 mods with HEI integration.

Yes, test show that with ultraLowMemoryUsage set to false there is no PackagedAutoJEIPlugin.onRuntimeAvailable() called at all.

After looking at JEI code, this is probably caused by some mods modifying recipes during onRuntimeAvailable, resetting the visible category list.
Without PackagedAuto, I would guess that this stalling would probably be experienced during play when one does a first recipe search.