According to some sources, Russia has already taken key parts of Bakhmut. According to other sources, Ukraine has pulled troops out. According to other sources, Ukarine has just relieved some troops, but left the garrison equally heavily defended. According to other sources, Ukraine has lost about equal to Russia due to heavy Russian shelling. And according to other sources, Russia has (as you say) lost a lot of troops so far trying to take the town.

What's the truth? We'll probably never know.

What is known is that Ukraine has/had about 30,000 troops in Bakhmut, making it one of the most heavily defended cities in Ukraine, if not "the most" as a percentage of soldiers compared to the pre-war civilian population.

30k troops and 8 years to build defenses. No conquering of such as small, heavily defended town would be quick.

We'll see better (but still not perfectly) in a few more weeks whether Russia has taken the town.

All that is to say I agree with your analysis, except for heavy Russian losses, as there has been no independent corroboration of that report.