I think 056 doesn't so much replace 037 as supersede it, because the missions of PLAN has changed.
Of the missions 037 was designed for, some have passed onto 022 catamaran, others became superfluous when Chinese navy had pushed the zone of likely low to medium intensity from the border region between brown to green water region 037 was designed for, to blue water beyond the comfortable reach of 037. So 037 kind of boat is now an ill fit for PLAN needs.
The new missions for PLAN require 056 type asset with more staying power, more range, and more mission flexibility.
In a way yes, though I'm more incline to believe that for a long time the PLAN had no choice to "do more with less", that made the 037 series perform in roles it wasn't primary anticipated for. The 037 series never designed for endurance or heavy firefights, if heavier firepower is needed then they'd need to bring out the 053 series and those have deeper draft means restricted sea routes are available in the case of disputed regions within SCS, and neither the 053 is optimized in endurance, plus the baseline platform also outdated by today's standard.
022 FAC is primary an attack craft, not patrol vessel so that rules out as well.
For the 056 corvettes, despite what "a certain bald old man" dizzing it as a mediocre platform, the 056 offers an updated baseline hull that's more suitable for the PLAN's defensive need in terms of low intensity conflicts and such, with better potential to branch into other specialized roles, support for helicopter (none of the 037 has it, and only a handful of the 053 series could) and better automation.
Still, by my visit to the new boats in July, I do agreed that they should get rid of any and all wooden (or wood like synthetic substitute, even if fire-retardant treated) stuff on the ship's interior.