I'm not going to touch the other ships with a 10-foot pole, except for Discovery itself. The ship was designed in the '70s and looks like it could fit into the TMP Era.
The Enterprise was commissioned in 2245 and TMP is in 2272-ish. If the five-year mission ended in 2270 as per VOY's "Q2" and TMP is 2.5 years later, it mathematically can't be 2271 like the Star Trek Chronology says.
Discovery being launched in 2256 and looking so close to a TMP-ish design is pushing it a little bit (you'd think it would be a design from closer to 2270) but it was still chronologically launched after the Enterprise so, in-universe, the design fits between "TOS" and "TMP", as it was designed in real life. So I'm not bothered by it.
You have to think of the pre-refit Enterprise as a 2240s design, not a 2260s design.