The main lounge (only lounge) at Mingalardon Airport (RGN) is the Mingalar Sky Lounge.
For Yangon, its pretty good. Only a couple of years old. Priority Pass accepted.
Good freshly cooked food options, basic bar with wines by the glass and basic spirits, beers etc. Lots of seating, plenty of power points, and a spa down the other end.
Can't recall if they have showers - do you want me to find out? As I can call them to check.
For arrival at 10.00am and a late afternoon check in - I'd suggest going downtown. Have lunch at one of the better heritage restaurants.
To kill an hour or two - find the nearest major shopping mall (eg Junction City, Myanmar Plaza, etc) and find the "Tony Tun Tun" chain beauty salon. Get a hairwash with head, arm, shoulder massage and relax for less than $6. Or similar for a full foot/leg massage. The whole lot for around $10 and a relaxing couple of hours - bargain.
So you have nothing else on for the half day in Yangon - just arriving morning and departing evening? Let me know what kind of things you are interested in and I'll give you more specific suggestions
Cheers