For Serbia, these (two) months are july and august where you can expect such situation. People go away from their jobs mostly for two weeks during that time.
At least in Bulgaria — hardly. July and August, and sometimes early September are traditionally reserved for summer holidays, but people rarely are away for more than a few weeks. Businesses continue to function as usual — industry, banks, institutions, etc., even with reduced productivity, and of course all tourist attractions are in full swing.
The last year it was possible to find hotels and accommodation in Bulgaria on short notice, but I’m a native, so things might be different from your perspective. I’d avoid the end of July and beginning of August (most people tend to go to a vacation then, and it’s also the hottest), and recommend going for a late August/early September trip. Basically all of the resorts will still be working, the weather is not so hot and the crowds are noticeably sparser. The prices could also be somewhat lower.
Your mileage may vary for other countries, though.
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