Don’t mix cleaning products - can make toxic gases - use one product and rinse well.

Rubber gloves - the old fashion yellow rubber gloves are good to protect your sensitive hands. Maybe wear glasses to protect your eyes from splashes.

Those acrylic plastic tubs are a beast to clean.

Magnet sticks to side = enamel on steel tub

I avoid mixing chemicals or products - but the Dawn sounds like it would work well simply because it cleans dirt, grease and grime. I use Cascade and diluted in warm water - after a bath - then rinse.

Enamel over steel tub.