Notice period of 90 days. Wow. That is a lot many days.
In many organizations, Performance Improvement Plans (PIPs) are frequently used as a procedural method to facilitate an employee's departure from the company. Managers often utilize PIPs to signal to an individual that they should begin actively seeking a new role elsewhere.
In your situation, I recommend either exploring the possibility of transitioning to a different team within the company, but it would be advisable to consult with the prospective team's manager beforehand. Alternatively, if an internal transfer is not a viable option, it may be prudent to commence your search for a new role externally. You needn't be overly concerned about the relatively short tenure at your current employer. More often than not, recruiters base their hiring decisions primarily on an individual's skills and qualifications, rather than the duration or rationale behind their previous employment periods.​​​​​​​​​​​​​​​​