The most recent USPSA list of "approved" pistols for Production class I can find is 4 years old.... is the P365XL approved for Production class?

Most likely.  Even it wasn't I'd just show up and shoot it.  No one would care.

From the USPSA Production gun list


SIG
Website: www.sigsauer.com
Notes: No SAO (Single action only) versions are approved. No models allowed with Blackwater custom magwell grips, or others that extend down to form magwells. 226 and 229 Legion models added 6/20/2016 5/27/2020 All calibers and models of the Sig Model P320 modular line are allowed in compliance with current rules governing caliber, and magwells, with and without manual safeties. X-Five Legion is the heaviest model at 41.7 ounces. P229 Nitron DAK 9mm/.40 added 9/9/16 5/5/17 Sig 320 X5 added: Magwell must be removed for Production and Carry Optics, weight is with magwell removed. Magwell is not legal for Carry Optics or Production. P320 X Carry, P365, and P320 X-VTac added 5/31/18. P320 X5 Legion added 7/15/19, weight is without magwell. 12/2/19 P226 LDC Added 5/27/2020 All calibers and models of the Sig Model P365 modular line are allowed in compliance with current rules governing caliber, magwells, etc., with and without manual safeties. 365-9-SAS and 365-9-BXR3, both with or without manual safety added. WCP-320 added 5/27/2020

   365-9-SAS, with/without manual safety (18 oz.)
   365XL-9-BXR-3 with/without manual safety (all variations) (21 oz.)