The Verdict: Not eligible
Costa Rica has no work route without a Costa Rican employer, so this is closed for now. If you keep a job abroad, look at the digital nomad stay; otherwise look at retirement or investment.
There is no points test, job-seeker permit or self-nomination. Every work category in Article 79 of the migration law runs through a company established in the country, and Article 80 makes the immigration department authorise the specific work.
Looking for work on a tourist entry is no shortcut: working on it is unlawful and makes a later application harder. The sequence that works is the offer first, then the employer files, then you move.
The digital nomad stay needs USD 3,000 a month from an employer or clients abroad, but it is a stay and its time counts towards nothing. Rentista (USD 2,500 a month of non-salary income), pensionado (a USD 1,000 pension) and investment are residence and do count.