If removing the floor tile without damaging the heat coils is not possible, then simply select a new tile and go directly over the tile floor. Remove the tub and the wall tile and replace it also. No sense doing a half remodel. Use a large format tile.

Your biggest decision is to determine how to address the window. See these examples to help make a decision.

Draw the bath as is and add all the dimensions. A heated floor is simple to replicate, so unless you are in love with the "perfectly good" tile, don't base a bath on it. Sometimes.....it is just easier to start over, there are great tiles at many price points. : )

Question to the pros: Could they remove the tub and keep the floor? Use some tile that would work with the brown? Seems like the budget is a concern. I have a friend who just covered bath tile with a spray on product done by a professional. They actually had both the tub and the tile sprayed. Looks nice, not sure how durable. Surprised.
I would definitely install a glass door, which would take up less space than the shower curtain. Personally, will never use another jetted tub...
Love the view! The window ideas are great. Would definately keep the view.
What color IKEA? I would be tempted to try to find IKEA look in traditional cabinet company.
Good luck!

Well you essentially have a shower by that window so I don’t understand your comment about concerns converting to a walk in. I think you need to step back and research accurate pricing for your area. Talk to a couple of GCs and get a full bath gut remodel vs just shower and vanity price. Budget will determine next steps as you will get a million different responses as to keeping or changing the floor. Nice view out that window!

You need to post a measured drawing of the bathroom footprint if you want relevant comments. We also need to know your actual maximum budget.
I hope you have been saving money toward this project because it will not be cheap. If you plan on using your credit card to pay for it, and you fail to pay off your whole bill monthly, you will be adding significant interest to the job cost.
Issues to consider:
The bathroom looks dark, dated and worn. Decide on a lighter, more reflective, color scheme.
Keeping the plumbing in the same positions will help keep costs down, but be sure to have the plumbing inspected by a pro because it makes no sense to do a new bathroom with old plumbing underneath it.
You will need to decide how to give a person in the shower some privacy. Some excellent ideas have been shown already.
Replacing the floor tiles over the heating element should not be impossible...but you will need a professional to do the job.
Include lighting improvements in your plan.
We await your drawing and your budget info.

Thank you for all the helpful comments

It is very difficult to get tradespeople on our island. I can book the person who did my other bathroom for May 2020, but tradespeople won't come to do quotes as they are all so busy right now. It's a bit of a strange situation as I will have to buy all the fixtures and tiles myself. The contractors who would do a full job are building houses and not interested in small renos. There is a waiting period of two years to have a house built.

I thought that I would get a start on planning it now. Yes I do not want to spend too much money on this reno. The other bathroom cost $15,000.

I don't want to change the window (because of cost)- a shower curtain in front of the window protects it from too much water. There is no issue with privacy. I agree that the bathroom isn't that nice but the main issue is that the fixtures are wearing out. I hate jetted tubs and we don't use it but we can't resurface the bath because of the jets.

I love the last photo (Beverly), thank you for the inspiration. That would be my ideal and I will see about getting that costed.

I will work on a scaled drawing, in the meantime thanks to all who responded for taking the time to help me.

Keep in mind you can't change out the wall plumbing valves etc without breaking through the tile, so you might as well change it. If you don't currently have any leaks, doing work in the area may cause a leak. It seems to always happen like that.

I would consider it shade of green for the walls.

a shade of green, not"it".