See also Dartmouth College v. Woodward argued for Dartmouth by none other but Daniel Webster.

Among other things Supreme court chief justice "Marshall concluded that Dartmouth’s [royal] charter constituted a contract and that New Hampshire had violated this contract in attempting to replace the original trustees." https://www.mtsu.edu/first-amendment/article/729/dartmouth-c...

Yes, generally the laws in effect before a colony or territory became a US state remained the same after they became US states. Contracts signed before statehood remained valid after. Property deeds remained valid. The criminal laws remained in effect. And so on, at least until amended by the new state legislature. Doing anything else would just be chaos, really. Louisiana is another example; its legal system has a distinctly French character to this day.

The treaty has not been fully followed, even according to the US government.

https://www.gao.gov/products/gao-04-59

Here in NM, a significant number the original Spanish land grants were ignored and replaced by new grants to (generally) Anglo owners. Fortunately, some of them were sufficiently cogniscent of the paradox of colonialism overriding colonialism that the new grantees re-issued (smaller) grants back to the owners under Spanish or Mexican law.

Ironically, there were also some Spanish land grants that took so long to process, Mexico had already declared independence from Spain before the legal process was complete, and this left a number of them in a strange form of legal limbo at the time of the treaty.