You're right on the transfer window not opening until later but it won't stop clubs announcing signings - think the date has previously been earlier but there's been some tightening up to ensure the window is only open for a set number of weeks (12?) in line with other countries.I don’t think the EFL transfer window opens until 10th June, so although we may hear something about out of contract players incoming I don’t suppose they, or any transfers involving a (small) fee, will able to be confirmed until after that.
Although that dates probably coincides roughly with our return to training?
However it won't stop clubs announcing signings - they will just be transfers effective of the relevant date (and subject to international clearance, etc.) Bolton have announced a defender from Cambridge today - I didn't look at the smallprint on their OS but suspect it's on that basis.
You're also right in the sense that in reality most clubs at our level won't complete many of the sort of signings you're talking about before July - given that out-of-contract players get an extra month from their club as a sort of notice period after their deal expires in June; and on that basis it generally isn't in the signing club's interests to do stuff too early (there are exceptions where players are in high demand and moving up the footballing food chain, etc.).