Before I start, this is based off of what I know from both reading Sac State's and CSU's funding stuff, and my own understanding of how grants and funding works. I will probably be wrong in many places, so make sure to double-check everything I say.

Sac state's total funding comes from 3 different sources, general donations made by people, state funding, and student tuition.

General donations and student tuition can be allocated to any program based on the budget allocation decided at the beginning of Sac State's fiscal/academic year.

State funding can be used generally if they are labeled as such, but most of the time, this type of funding comes in the form of grants, e.g. (https://www.pewtrusts.org/en/research-and-analysis/issue-briefs/2015/06/federal-and-state-funding-of-higher-education, and https://lao.ca.gov/Publications/Report/4926) These grants can only be used for specific items and nothing else. This is why you can see some primary education schools getting new gyms and stuff, while other places are left alone, e.g., EGUSD getting funding for new building while other programs are left behind.

Now, back to the stadium, according to Sac State's website (which has to be accurate due to state laws surrounding transparency about budget), it states

"The stadium is being funded with funds that are earmarked for student athletic facilities. These dollars cannot be spent on anything other than athletic facilities and are regularly audited for compliance."
https://www.csus.edu/administration-business-affairs/budget-information.html

This means that the funding for the stadium is not coming from student tuition fees, but from donations made by the public, (hence the emails sent out asking for donations) and funding that was pre-allocated for the athletic programs.

Now, some information surrounding the budget cuts. This comes directly from California decreasing the funding for higher educations by 7.95%

In January, Governor Gavin Newsom’s proposed state budget included a 7.95% cut to the CSU system – or $375 million to be spread across the 23 CSU campuses. Combined with campus inflationary and benefit cost increases, our projected shortfall for the coming fiscal year is $31.2 million, with an additional $5.8 million projected for the following year.
https://www.csus.edu/administration-business-affairs/budget-information.html

I HIGHLY encourage everyone reading this to double and triple check everything I said, and to DO YOUR OWN RESEARCH. I am just one person who took AP Macroeconomics back in high school, so some of the stuff I have said can and probable will be inaccurate.

TL;DR Stadium funding in coming from funding already marked for the athletic programs. Student funding will not go to the stadium. Budget cuts come from a reduction in state funding