They also said the the Eugenics War and World War III were one and the same, supposedly in the late 90's. Yet everything since Wrath of Khan has shown the Eugenics War/World War III as being a mid 21st century event.
Strange New Worlds is hardly responsible for the change and is just going with what has been pretty firmly established.
In all fairness, SNW somewhat combined everything. Pike mentions three conflicts, which he implied were building blocks to a whole.. to paraphrase, "First there was the Second American Civil War, which lead to the Eugenics Wars and eventually, just World War Three." There's basically three distinct conflicts that in the end, are all lumped under "WW3".
As mentioned, SNW has "graced" with the fact that timelines are officially messed up, so "canon" doesn't really matter anymore and nothing makes sense anymore. BUT... to answer the OP, in the timeline that SNW takes place in, no. There was no Enterprise from NX-01 to 1701, this is explicitly mentioned.
So we have about an 80 year stretch with no Enterprise. It's not THAT unbelievable though. NX-01 was a big deal for Earth, but in the grand scheme of the Federation, the ship wasn't overall that big of a deal. Archer was important to the Federation, but Enterprise is more Earth history. It's NCC-1701 that became the legendary Federation ship.
To go on a conjecture tangent... NX-01 may not have been retired in 2161, but also may not have been a Federation ship. We've known for decades, but LDS and DSC solidified it, member worlds operate their own fleets as well in addition to Starfleet. PIC S2 and 3 suggest that NX-01 eventually got the NX-Refit (the model shows up, it's "supposed" to be Enterprise although it's never actually confirmed on screen.). It's
possible that post-Federation, Earth still maintained an independent fleet apart from Starfleet... with NX-01 being assigned to Earth Defense Force and getting it's refit.
It reconciles two seemingly contradictory things while also offering an explanation why it took so long for another Enterprise to show up. It still fits with the E-D computer not acknowledging NX-01 as a Federation starship when Scotty asked. It fits with PIC S2-3 of NX-01 getting the NX-Refit. And... if NX-01 continued to serve in the Earth Defense Force for another decade or two, the timespan between Enterprises is a bit lower. Say it served until... 2190? Just throwing a number out there. 1701 launched 2245... factor in a few years for development and construction, and i'm assuming Enterprise was a first-run Constitution... say the ship was planned closer to 2235... 40ish years with no Enterprise.