Build quality and problems

Just guessing, but if a full reset to factory defaults plus deleting all data, reinstalling Garmin Connect and removing the HRM-Pro and Fenix 6 from the Bluetooth settings on the phone did not help, then try if activities without the Pro do sync correctly.

I’m assuming that Connect and your 6X both have latest updates applied.

With your 6X connected to computer, check Activities folder. Are all your activities there? Copy them to a folder on computer. 

I’ve got a few suggestions.

Remove your HRM Pro as a device in Connect.

for the bit where Bluetooth on phone is showing connected but 6X not showing in Connect - remove your 6X from phone Bluetooth menu then Add Device via Connect with your 6X in Pair Phone mode. 

Add Device for your HRM Pro to sync to Connect again.

because you now have  2 devices in Connect, make sure your 6X is Primary Device.

If I don't use the HRM there is no sync problem with Garmin Connect

My F6X is my primary device and als has the latest official SW updates.

I already removed HRM from F6X and Connect and added it afterwards without solving the issue.

Do you have your HRM pro connected to your phone or to your fenix? Have you tried clearing the cache of your Garmin connect app? 

There is also a whole thread about sync trouble shooting: https://forums.garmin.com/apps-software/mobile-apps-web/f/garmin-connect-mobile-andriod/220202/sync-connection-troubleshooting-guide

This is going to sound a bit strange, but what happens if you wait before saving an activity (that you did with the HRM-Pro), until you have stored the HRM-Pro far away (out of Bluetooth range of your phone and watch), then save the activity, and then wait until it syncs? Instead of storing the HRM-Pro > 10 meters away, you can put it in a fully closed metal container or in a microwave oven (obviously, don't switch it on).

HRM is only connected to my F6X

Saving the activity goes without any problems. It start after when I saved my activity and then a few moments later take off the HRM. From that moment it's not possible anymore to sync the F6. Only a restart will make it sync again but then all the data between taking off the HRM and restart is gone.

I'll get back to this. I have an idea what it may be but don't have time to explain at the moment.

In your first post, you wrote: "In my Bluetooth settings it says that the F6X Pro is connected and in Garmin Connect app it says not connected.". Is that still the case? It is definitely not good. Double check there is no other (old) phones or tablets around that run Garmin Connect and had your watch paired to it in the past.

Another thing is the fact that syncing after an activity works as long as the HRM-Pro is not near. Is the HRM-Pro connected to your watch via Bluetooth? If so, try to delete that connection and have it connect via ANT+ instead.

Nothing about this is documented, so this is a guess: the HRM-Pro may be keeping the watch busy with communication about downloading stored HR data. This results in the watch 'thinking' the activity is not complete (because stored data may be still get downloaded), and the watch will not sync an open activity file. You can reset the HRM-Pro by taking out the battery for a minute. If the problem recurs, best to connect Garmin Support and mention that you suspect that the HRM-Pro has a problem (because syncs works, as long as the HRM-Pro isn't connected to your watch at the time of the sync).