Joyce et al. 2021 report,
“Over the last 25 years, researchers, mostly paleontologists, have developed a system of rank-free, phylogenetically defined names for the primary clades of turtles. As these names are not considered established by the PhyloCode, the newly created nomenclatural system that governs the naming of clades, we take the opportunity to convert the vast majority of previously defined clade names for extinct and extant turtles into this new nomenclatural framework.”
As long as Joyce et al. are working within a valid phylogenetic context, this sounds like a great idea!
“We are confident that we are establishing names that will remain accepted (valid in the terminology of the ICZN 1999) for years to come.”
Well, let’s see if Joyce et al. followed a valid phylogenetic context.
Archelosauria Crawford et al., 2015,
“The smallest crown clade containing the archosaur Crocodylus (orig. Lacerta) niloticus (Laurenti, 1768) and the turtle Testudo graeca Linnaeus, 1758, but not the lepidosaur Lacerta agilis Linnaeus, 1758 (Fig. 1b).”
Not a good start. In the large reptile tree (LRT, 1796+ taxa; subset Fig. 1) the smallest clade that includes Crocodylus and Testudo is a junior synonym for Reptilia (= Amniota). Joyce et al. are not familiar with the basal dichotomy that split reptiles into Lepidosauromorpha (lepidosaurs + turtles) and archosauromorpha (mammals and archosaurs) in the Viséan with Silvanerpeton as the last common ancestor. What can be done when turtle experts don’t agree (see below) on the origin of turtles?

Figure 1. Carbonodraco enters the LRT alongside another recent addition, Kudnu, at the base of the pareiasaurs + turtles.Figure 1. Carbonodraco enters the LRT alongside another recent addition, Kudnu, at the base of the pareiasaurs + turtles.
Joyce et al. continue:
“Comments—The name Archelosauria was recently introduced by Crawford et al. (2015) for the clade that unites Testudines and Archosauria Cope, 1869b [Gauthier and Padian, 2020] exclusively.”
That was a mistake due to taxon exclusion. Don’t accept mistakes that put you into an invalid phylogenetic context.
Ankylopoda Lyson et al., 2012,
“Definition—The smallest crown clade containing the lepidosaur Lacerta agilis Linnaeus, 1758 and the turtle Chrysemys (orig. Testudo) picta (Schneider, 1783), but not the archosaur Crocodylus (orig. Lacerta) niloticus (Laurenti, 1768)
In the LRT that clade is the Millerettidae (Watson 1957) with Milleretta as the last common ancestor.

Figure 2. Milleretta, a Late Permian descendant of the Late Pennsylvanian ancestor of turtles and Eunotosaurus.
Joyce et al. continue:
“Comments—A clade consisting of Testudines and Lepidosauria Haeckel, 1866 [de Queiroz and Gauthier, 2020] to the exclusion of Archosauria has been retrieved in a number of phylogenetic hypotheses (e.g., Rieppel and Reisz 1999; Rieppel 2000; Li et al. 2008), but was only named Ankylopoda relatively recently (Lyson et al. 2012).”
What can be done when turtle experts don’t agree (see above) on the origin of turtles?
Testudinata Klein, 1760
“Definition—“The clade for which a complete turtle shell, as inherited by Testudo graeca Linnaeus, 1758, is an apomorphy. A ‘complete turtle shell’ is herein defined as a composite structure consisting of a carapace with interlocking costals, neurals, peripherals, and a nuchal, together with the plastron comprising interlocking epi-, hyo-, meso- (lost in Testudo graeca), hypo-, xiphiplastra and an entoplastron that are articulated with one another along a bridge” (Joyce et al. 2020b: 1044).
In the LRT (subset Fig. 1) soft-shell turtles (Fig. 3) had a separate parallel origin alongside hard-shell turtles (Fig. 4). Their last common ancestor had no shell: the pareiasaur, Bunostegos (Fig. 4). Workers like Joyce et al. 2021 are working under an assumption that is not true. Turtles are not monophyletic. You can read that manuscript on ResearchGate.net here. Turtle workers did not let this get published.

Figure 3. Soft shell turtle evolution featuring Arganaceras, Sclerosaurus, Odontochelys and Trionyx.

Figure 4. Another gap is filled by nesting E. wuyongae between Bunostegos and Elginia at the base of hard shell turtles in the LRT.
The remainder of Joyce et al. 2021
lists and defines various clades of turtles. Without a clear understanding of parallel turtle origins, even some of these are subject to change when pertinent taxa are included. Most will likely remain the same as they distance themselves from turtle origins.
References
Joyce et al. (15 co-authors) 2021. A nomenclature for fossil and living turtles using phylogenetically defined clade names. Swiss Journal of Palaeontology 140:5 https://doi.org/10.1186/s13358-020-00211-x