Sony has released their first firmware update for the new WF-1000XM4. The version is now 1.1.5 and this update improves Bluetooth connection stability. Reading some reddit posts, it looks like some people have issues installing the firmware but I suspect this might be down to the earbuds powering down and the install failing.
Update instructions can be found here.
The most important thing is to keep the headphones turned ON and not have them turn off during the update.
In the Sony | Headphones Connect app, set the Automatic Power Off function to Do not turn off. Once you have updated your headset, you can change this back to conserve battery when the headset is not in use. Make sure that both devices, phone/tablet and headset are fully charged.
If an update error message appears, press OK, insert the earbuds into the case and then take them out to restart them. Then restart the Sony | Headphones Connect app and try the update again.
With more and more people getting their hands on the new headset, more issues/bugs will show up and Sony will have more firmware updates. I would expect more improvements to connection stability and improvements as time passes.
As always post any update issues here or Reddit in the Sony subreddit or the headphones one.