To wrap up this question… no, Wizards Unite classes are not similar to Pokemon GO teams.
In Pokemon GO teams compete against each other and you can only benefit from bonuses / gyms players from your own team.
In Wizards Unite, all players are on the same “team” and classes (aka Professions) allow them to play different roles. Having different classes in Fortresses is essential, similar to regular MMOs where you need a healer, a tank and a DPS.
Moreover, you can (and should) switch between Professions actively to fill out whatever the need of your group currently is.