Partner's UK Graduate VISA Ending: Options?

My partner is Nigerian and her 2 year graduate VISA is ending on May 31st. She has been trying to get a sponsored job to no avail.

What are options on extending her stay in the UK? We have been living together since 1st May 2023 which will be two years at the point of VISA expiry. And our relationship preceeeds that by one year (we are not married though and no kids). Is a spousal VISA our best route to allow her to stay? We have photos of us together to prove that but not posted online... so how can that be used as proof?

I earn over £29k if that helps.

Does anyone know our options as I found the gov website a little confusing. Have we left it too late to extend her VISA or is there still time? And is it worth contacting a professional or is it an easy process to complete yourself?

I'd really appreciate any feedback someone can give. I love her very much and want her to stay.