Jason Torchinsky, Steve Roberts, Dennis Polio, and Andrew Pardue write in the Harvard Journal of Law and Public Policy:

In recent months, Donald Trump and his supporters have stoked rumors that he may run as
a third-party candidate for president in 2024 if he fails to win the Republican nomination. These
rumors, sometimes bordering on outright threats, have reinvigorated a discussion of sore-loser
laws—restrictions that states place on candidates running in the general election after losing a
primary election. This discussion has centered on two questions: 1) whether sore-loser laws apply to candidates for president, and, if so; 2) whether a Trump third-party campaign can win a majority of electoral college votes if sore-loser laws prevent him from accessing the ballot.

This article explores the hypothetical scenario where Trump (or any other Presidential candidate) seeks to run in the general election after a losing bid for a major-party nomination.
Although nearly every state now has some kind of sore-loser restriction, their potential
application to presidential candidates has not been extensively studied. The Authors have determined that sore-loser laws in 28 states do indeed apply to presidential candidates and that if a candidate fails to win the Republican nomination, sore-loser laws will prevent access to the general election ballot in those states. This includes 20 states that Trump won in either 2016 or 2020 which total 225 electoral votes—more than 83% of the electoral votes needed for a majority.

As a result, it would be nearly impossible for Trump to win the general election as a third-party
candidate given the limited number of Republican-leaning or “tossup” states where his name
would appear on the ballot, which together amount to an insufficient number of electoral votes
for a general election victory. Accordingly, any third-party presidential campaign mounted by
Trump or any other defeated Republican could only function as a spoiler campaign—splitting
the vote that would otherwise coalesce behind the Republican nominee—thereby causing that
nominee to lose the general election.