In a comment above, ohwilleke points out, "Some of the cases Trump has appealed are criminal cases."
This answer addresses a reason that a state may choose not to appeal a criminal case that has been dismissed.
A state can choose not to appeal a dismissal of a criminal case in a local court in which a state law was found to be unconstitutional as applied, but which, being the lowest court, does not establish binding precedent for future cases in that state. The state may fear that, if appealed, a higher court could sustain the decision and find the law unconstitutional on its face, which could establish binding precedent, overturn a longstanding statute and call into question numerous past convictions under said law.
We have a recent example. Mr. Dean Donnell, a resident of New Hampshire with a New Hampshire license to carry a concealed weapon, was discovered during a routine traffic stop in neighboring Massachusetts to be in possession of a firearm in violation of Massachusetts G.L. 269 §10(a), and was arrested on felony charges. This statute makes it unlawful for any person in Massachusetts to carry a concealed firearm outside of their home unless the person holds a valid Massachusetts License to Carry a firearm (LTC). Massachusetts currently issues LTCs to both residents and non-residents, but does not recognize LTCs or permits to carry a concealed weapon (CCW) issued by any other state. Mr. Donnell had a New Hampshire CCW permit but did not have a Massachusetts LTC.
On August 3, 2023, Judge John F. Coffey of the Lowell, MA District Court, in Case No. 2211CR2835 (pdf) ruled that Massachusetts G.L. 269 §10(a), is unconstitutional as applied in this case in light of the recent U.S. Supreme Court case NYSRPA v Bruen.
The judge writes in his conclusion,
A law-abiding resident of New Hampshire who is exercising his
Constitutional right should not become a felon by exercising that
right while he is traveling through Massachusetts merely because he
has not obtained a Massachusetts license to carry . . . . This Court
can think of no other constitutional right which a person loses simply
by traveling beyond his home state’s border into another state
continuing to exercise that right and instantaneously becomes a felon
subject to mandatory minimum sentencing of incarceration. . . . An
individual only loses a constitutional right if he commits an offense
or is or has been engaged in certain behavior that is covered by 18
USC section 922. He doesn’t lose that right simply by traveling into
an adjoining state whose statute mandates that residents of that
state obtain a license prior to exercising their constitutional
right. To hold otherwise would inexplicably treat Second Amendment
rights differently than other individually held rights.
By Massachusetts tradition, appeals on adverse rulings in criminal matters in the lower courts may only be advanced through the Attorney General’s office. Thus far, that office is silent on the question of appealing judge Coffey's decision. It is notable that this may be the very first criminal case nationwide in which a judge ruled that, in light of NYSRPA v Bruen, a state must recognize a defendant’s LTC or CCW issued by another state.
So the Massachusetts Attorney General can either decide to let this one go or risk the eventual overturn of at least some aspects of Massachusetts gun law, potentially requiring Massachusetts to recognize all out-of-state CCW permits carried by non-residents, and if appealed further to Federal courts and the Supreme Court, it could conceivably lead to nationwide universal CCW reciprocity between the states. I’m sure the Massachusetts AG doesn’t want that on her resume.