Am I tied to one employer on this card, and what happens if I want to change jobs?

The shortage-occupation Red-White-Red Card permits employment only with the employer specified in your application, so it is employer-bound. You may take on subsidiary self-employment if the legal conditions are met, but your main job is fixed to that sponsor.

To gain unrestricted access to the Austrian labour market and the freedom to change employers, you apply for the Red-White-Red Card plus. According to the official source this becomes available once you can demonstrate roughly 21 months of qualifying employment within a 24-month window. Until then, a change of employer typically requires a new authorisation, so discuss any planned move with the authorities before resigning.