My job offers "free" online consultations for mental health reasons. Every single "available" slot is during working hours.

Based on the text in your image i assume that you live in the Netherlands. I would advise you to discuss this with your employer. As you are unable to plan a needed psychiatric appointment during working hours you have the right to take some short leave time for that.

Sources: https://www.rijksoverheid.nl/onderwerpen/arbeidsovereenkomst-en-cao/vraag-en-antwoord/wanneer-heb-ik-recht-op-bijzonder-of-buitengewoon-verlof#:~:text=Verlof en doktersbezoek,recht hebben op kort verzuimverlof.

https://www.rijksoverheid.nl/onderwerpen/calamiteitenverlof/vraag-en-antwoord/duur-calamiteitenverlof#:~:text=U kunt calamiteitenverlof of kort,kort verzuimverlof in een jaar.