I guess, the wave of new members signing up has already passed. The servers seems stable enough right now, though there are some complaints of poor connection as usual.
Your worries could be correct as well, but only time will tell.
Right now don't worry, and just enjoy the game! 
chess.com has lot's of people on it because of COVID-19
I'm worried that we might have a flood of server problems very soon.
I think they already started months ago. There were several problem days.
I believe they have taken steps to minimize future server breakdowns. https://www.chess.com/blog/erik/chess-com-during-this-global-stay-home-moment
chess.com has lot's of people on it because of COVID-19
I'm worried that we might have a flood of server problems very soon.
I think they already started months ago. There were several problem days.
I believe they have taken steps to minimize future server breakdowns. https://www.chess.com/blog/erik/chess-com-during-this-global-stay-home-moment
But I think it was because of 24 legends of chess. Lots of people got on chess.com to watch it; so I think 24 legends of chess was the case
chess.com has lot's of people on it because of COVID-19
I'm worried that we might have a flood of server problems very soon.