Yes, new car prices have gone through the roof but so has the value of your trade once it is repaired.
I just checked mine at KBB.com. 13,200 miles, I designated excellent condition, and it shows a midpoint trade value of $29,900 for my zip code. That's $130 more than it's original sticker price, and that's the highest figure I've seen with quarterly checks. Nuts.
EDIT: I started looking at at trading into a comparable 2022 2.5 Select S stickering at $30,245 with only splash guards added. That $29,900 trade value is in error. I might have selected Touring w/ Preferred or made some other error. The actual figure is $28,604, $1,166 under original sticker, still nuts for a two year old vehicle. However, that's probably not a plausible trade credit given what I'm seeing advertised for near-comparable CPOs. I'd probably be negotiating up from very good condition @ $27,706. I doubt I could squeeze the spread under $2,000 after tax on the difference and $75 prep. If I kept cars for 3 years it would be a no brainer.
Mazda is on track to report another record for CX-5 USA sales and is on track for record numbers for Mazda USA in total going back to 2005 which probably accounts for some recent buyers reporting purchases at or a bit under sticker. Why not less? Probably because other makes / models in this class are still suffering with low production whereby prospective RAV4 buyers, to take one example, are jumping to Mazda where there is some lot availability or shorter wait times thereby juicing demand.
Though you are moving on from Mazda there is a moral to this story. If your price sensitivity is high, check sales volumes of models under consideration. Those that are ramping back up to pre-pandemic levels, if any, may have less onerous pricing.
CX-5 sales:
Mazda CX-5 Sales Figures
RAV4 sales:
Toyota RAV4 Sales Figures
CR-V sales:
Honda CR-V Sales Figures