Dance in the shower?
Even fairly restrained dancing over an extended period can elevate your heart-rate and trigger many of the benefits of exercise.
If you have a shower and live in an area where cold water is provided for free, then there is no cost. Additionally, this should address your sweat issue much like swimming in a pool.
It is indoors which eliminates sunlight.
Vis-a-vie the boredom constraint. Dancing to music by itself may be a varied enough activity to keep you mentally engaged. If this is insufficient you might consider audiobooks or talk radio.
Complications:
Safety. If you dance too vigorously then you may slip or injure yourself. You will know better whether this is a very likely issue. If it is, you may be able to mitigate with protective clothing (either purchased such as no slip water-shoes/socks or made from household objects; feasibility depending on your particular budget constraint and safety concerns).
You may not have a sufficiently strong set of external speakers to overcome the noise of the shower. If so, you might mitigate by (1) reducing the water flow for your shower, (2) purchasing or building louder speaks (for example, build a cone out of cardboard to amplify and direct the volume.)
Just cold water may be too cold for you. To mitigate either (1) add hot water (and possible add cost), (2) exercise outside the shower first to raise your body temperature, (3) acclimate yourself to colder water (this has been done by many people in the past either by necessity or due to a specific purpose such as Channel swimming).
I doubt I could hear anything with content over the shower itself no matter how good my speakers were, and I have pretty terrible balance in general. (I rarely actually fall, but I have to touch walls a lot to make that not happen.)
An exercise:
Name something that you do not do but should/wish you did/are told you ought, or that you do less than is normally recommended. (For instance, "exercise" or "eat vegetables".)
Make an exhaustive list of your sufficient conditions for avoiding this thing. (If you suspect that your list may be non-exhaustive, mention that in your comment.)
Precommit that: If someone comes up with a way to do the thing which doesn't have any of your listed problems, you will at least try it. It counts if you come up with this response yourself upon making your list.
(Based on: Is That Your True Rejection?)
Edit to add: Kindly stick to the spirit of the exercise; if you have no advice in line with the exercise, this is not the place to offer it. Do not drift into confrontational or abusive demands that people adjust their restrictions to suit your cached suggestion, and do not offer unsolicited other-optimizing.
To alleviate crowding, Armok_GoB has created a second thread for this challenge.