Here are 7 tips for cleaning grout: https://www.bobvila.com/articles/cleaning-grout/
I use hydrogen peroxide for grout, and an equal mixture of vinegar and water with a few drops of Dawn for the tub. Put it in a spray bottle, spray it on and let it sit for a while. It should come right off. If it needs something tougher, make a paste with baking soda and water. Apply that, let it sit for a while, they spray on the vinegar mix and let that sit 5 mins. That should cut through anything that is left. Wishing you the best.
This is a recipe for tub and grout cleaner that might work: https://www.google.com/amp/s/www.apartmenttherapy.com/how-to-make-your-own-bathroom-cleaners-shopping-list-recipes-108150%3famp=1
Hi ! Any cleaner with bleach in it will work , along with some elbow grease ! Using a grout brush will help , it is a cleaning tool that looks like a oversized tooth brush , with a curved top . Try keeping a squeegee in or near the tub area and use it to take off the excess water each time the bath/shower is used !!!! It almost totally keeps the area from building up gunk to clean ! Making cleaning quicker and less frequent !
also always allow the bathroom to dry out , by leaving the door and or window open
For at least 15 minutes after using , as well as using the exhaust fan , if you have one .