Are stable coins like USDT safe?

I want to buy some crypto for storing on my Trezor as an alternative to saving money in the bank. So I am not particularly interested in making a return – I just want my original deposit to be there, should I need it (I can handle GBP/USD currency fluctuations). So that rules out Bitcoin / Ethereum as they are just too volatile for my purposes.

I have heard of USDT / Tether and it seems to tick my boxes of being pegged to the dollar, but I have heard some bad things about it.

Should I just go with USDT or is there a better alternative for me?

EDIT:

Just to add, I do have some BitCoin / Ethereum and plan to buy more, but I also want to hold a small amount of crypto that is more stable, just for emergencies, as I don’t want to rely purely on banks for easy access cash.