Does Bq/L convert to mSv/year dosage?

Kudos for being confused. Seriously. That means you have recognized that there is an "apples to oranges comparison" going on and you are thinking about the consequences of that.

However, think not of one light bulb but instead think of one million tiny light bulbs. If they were sprayed on a wall and you face that wall, they will shine their light on the front side of your body. If instead they were absorbed into your blood stream and distributed throughout your body, their light will be spread somewhat evenly across many internal tissues. If you inhaled them they would be deposited in your lungs and while there just illuminate your lung tissues. If they all found their way to a small gland such as the thyroid, you'd have all their light concentrated in an even smaller area.

Of course, these tiny light bulbs also come in different colors! For example, the red "alpha emitter" bulbs emit light that can be blocked by dead layers of skin. Stand in front of a wall of them, no real worries. If they get into your body somehow... especially if they gravitate to one area... then you have something to worry about! Different colors of light are capable of penetrating our tissues to different degrees and the type of damage that is done is different as well.

OK, this is clearly getting very very complicated. All these details...exactly what someone is exposed to, how they are exposed, for how long, etc etc are of TREMENDOUS importance. BUT, we can't go around doing a complex analysis for everyone who is exposed to something. That is too hard... it would take too long... it would be too costly. Hmmm. How about we assign simple "weights" to the different color light bulbs, which we think are somewhat representative of the harm they can do and how about we assign "weights" to some different types of tissues which we think are somewhat representative of how sensitive the tissues are to light. Hurray! We can now do some far easier analysis to arrive at a single number that we think will to some limited extent describe the risk from different types of exposures.

A very crude analogy I admit, but that is the concept. We've all seen comparisons of apple A to orange B... these comparisons are rooted in the idea that a simple weighting scheme is sufficient to describe actual risk. People... professionals... are taught this approach and it is in wide use. Most simply accept it rather than prove its legitimacy to themselves before using it. It makes their life easier... it is a "standard approach" and if they stick to a "standard approach" they have that as an excuse if ever there is a liability claim. Others, though, truly engage in critical research and thinking and genuinely form legitimate views of their own.

How appropriate is this "standard approach"? How large is the margin of error that was created through such simplification? What is the history behind this... who created this methodology and how trustworthy are they and the process... what data supports it and what data contradicts it... how much can we rely on this approach?

That, I'm afraid, no one can answer for you. If you want, you can accept what others tell you to think. Maybe they are right. Maybe they are wrong. If you can find the time, it would however be best if you try to learn more and at least sanity check what you are being told.