Check the smell of your cold water vs hot water taps.
I had the same smell coming from my hot water heater... which I had not used.
I took out the anode rod from the heater and it was covered in something not quite animal, plant or mineral. And, it stunk. I cleaned the rod. I then had to flush the hot water tank. I even improvised a brush to get into the tank and try to clean the inside. That made a huge difference.
A week or so later, the smell started to return and I upped the percent of bleach in the fresh water tank and let it sit. That had the unexpected consequence of killing the black, evil growth in my fresh water tank and it started to detach from the surface of the tank.
It then clogged up my strainer... over and over. I ended up unscrewing the filter at the fresh water tank and taking a garden hose connected to a small diameter plastic tube and spraying the inside of the tank with higher pressure water. More black goop came out. Goop I had never smelled, but was a source of something that would continue to grow once that water went to the hot water tank.
Because my fresh water tank's support beams were bowed tremendously, I decided to drop the fresh water tank and replace them. When I got the tank dropped out, I carried it over to the side of my house were I used high pressure water, more bleach, soap and an endoscope for a couple of HOURS before I was convinced it was clean. I even improvised a brush that would flop around on the inside of the tank creating more friction. Oh, and I used pool bleach in powder form to add to the friction.
In the end, getting rid of the bad water smell required a full system flush and cleaning. Some of the pipes are impossible to reach, but now I have nice, pleasant town chlorinated water coming through the system.
I recommend you start with cleaning the hot water tank. If you've bleached your system and your water filter/strainer next to your fresh water tank isn't clogged, you might be ok. If it starts to get clogged from loosened junk, it's a symptom your fresh water tank is coated with bad stuff. (The $25 endoscope I got from Amazon was invaluable in peeking into the tank, by the way.)
Lastly, I ended up replacing the strainer with a Shurflo model that unscrews from the bottom for much, much easier cleaning. https://www.wholesalemarine.com/shur...SABEgJGuPD_BwE