You could place a plastic mat on top to limit evaporation.
You could also reclaim the water from the shower for use in the toilet by turning the supply to the toilet off and manually transferring it to the toilet tank.
There are lots of things you could do to save resources but most things are not done and are not going to be done because it is inconvenient and takes time, and time is money.
Edit: now that you have me thinking about this idea, it would be possible to have a container in the bathroom attached to a plug that has a hand pump and a tube going to the drain that could be used to reclaim and hold the water that could be higher than the toilet supply and the pressure from it could be used to have it self fill the toilet tank. The container could be highly conductive material like stainless steel and it could be relatively sealed to avoid humidity issues. This would of course be a vector for illness in some cases.
That was the original thought until I went off on the tangent about saving the hot water in a separate tank from the bathtub after it is "used" for the bath allowing the heat to be harvested and the water to be re-used.
The original post is about leaving the hot water in the bath to use the energy to heat the house or help heat incoming water. The idea of an external tank made out of conductive material would eliminate some of the problems and also allow the water to be re-used for the toilet.
Toilet cisterns arguably do reduce usage but then many people complain about less effective flushing which requires additional water; I don't have data to know if these objections are just a cliche or reflect an actual problem. My understanding is that lawn-watering is the biggest waste of water by consumers, to the point that some local authorities will subsidize people reorganizing their gardens to be more suitable for a dry climate.
Now, low-flow toilets have an amazing amount of research and design put into how to meet the guidelines while still performing as well as, and often better than, old 4+ gallon flushes.
A few (ill-informed) complainers aside, this actually seems like a win all around. Toilets don't cost more than they used to, they use less water, and perform better than ever.
We have a lot of leaky pipes. I don't get around as much as I used to but it's not uncommon for me to see a different leak every time I go for a walk around SE London.
https://www.theguardian.com/environment/2019/mar/18/england-...
This is radically underselling how much most people are willing to do for 50 pounds. If people are being squeezed out of their lifestyle due to energy costs (which seems quite likely, looking at the aggregate stats) they'd spend the time to conserve energy. Assuming someone shows them how to do it.
It remains a mystery why everyone was so calm walking in to this while tightening the screws on fossil fuel industries to stop them investing int he future. The globe needed a supportive regulatory environment for more nuclear power 20 years ago. Now there appears to be a global crisis in progress.
Because the only half-solutions we got for mitigating climate change were drafted by people who are largely free market types, and they can only envision free market solutions - which require end users figuring out how they are going to deal with more expensive energy on their own.
That does, of course, result in quite a bit of pain along the way.
Renewable haven't been cost-effective (or technically feasible in some cases, renewabled seem to have been a warning sign for incoming grid instability so far) and all the alternatives have been blocked by politics. I don't know about Europe's environmental legislation but it would be no surprise to discover even most renewable plays were facing legislative challenges too due to the area they take up.
For a market solution to work somebody has to be allowed build something and let it run for 20-50 years to reclaim the capital costs and make a profit. Speaking as someone who would quite have liked to be investing in energy plays about 5-8 years ago when the problem started to become apparent, the legislative environment in the west is too fraught to risk it. We weren't going to start doing anything useful until a crisis happened to get some political cover for the unpopular energy sources. Here we are, so now maybe something will get done.
Energy prices are so high because too many guarantees were given to too many parties to entince investment.
Sure the market is signalling that anyone who can bring energy to the table will be rewarded, and trying desperately to keep people in the game who are already playing. But there'd be capacity built and the aggregate numbers wouldn't look so bad if new construction hadn't been politically blocked for years now.
They're choosing de-industrialisation rather than letting people use nuclear or fossil fuels. People really should be panicking about that, they are going to take a massive lifestyle hit. There will be trouble.
[0] https://en.wikipedia.org/wiki/File:UK_electricity_generation...
[1] https://en.wikipedia.org/wiki/File:India_electricity_product...
Nuclear on the other hand is game over everywhere except China. It won't come back within the next 20 years. After this renewables and power grids optimized for renewables (across countries and with lots of decentralized storage based on electric cars) will make any type of energy generation which isn't wind and solar infeasible.
Nobody is choosing de-industrialization. Cheap gas from Russia has been keeping energy cheap in Europe. People are choosing solidarity with Ukraine even if this means some harder years.
An inline filter of some sort could be used for particles but that would require maintenance.
There would also be soap scum build up and hair conditioner products would gunk up the works I'm sure.
https://imgcp.aacdn.jp/img-a/1200/auto/global-aaj-front/arti...