Worn out chainring or missing tension

Chain tension is set by the springs in the derailleur. Some derailleur models have a tension adjustment in the upper B-pivot, but I think this is to adjust the range B-screw rather than change the overall force the derailleur puts on the chain.

I will focus on the chain tension part of the answer, as your big chainring is clearly worn out. However, do note that increasing the derailleur spring tension wouldn’t stop the chain skipping on the worn chainring. Therefore, this answer is mainly for the sake of interest.

By chain tension, I believe you actually mean the tension in the rear derailleur spring. This spring takes up slack in the chain. If your spring tension were too low, the chain could be slack in some or many gears. However, I don’t believe that it’s a setting most users need to manually change, as the factory tension is likely sufficient. From this Park Tools page on overhauling rear derailleurs, Shimano and Campagnolo RDs appear to have one setting for increasing the cage tension from the stock setting. SRAM appear to have one setting higher and one lower. I actually don’t know of any clear reasons you would want to increase the cage tension, but it is possible to do so. I suppose that if you were converting to 1x without a clutch equipped RD, you might consider increasing the cage tension, as discussed in this previous Q&A. (If you do this, you might consider using a chain guide as well.)

Less relevant to you, I recall that Friction Facts, an independent researcher later bought by Ceramicspeed, showed that all else equal, higher cage tension meant slightly more drivetrain friction, although manufacturers objected that the cage tension was necessary to ensure good shifting. I believe that Ceramicspeed’s oversized pulley cages contain at least one position which lowers the cage tension from the stock Shimano or Campagnolo setting. The amount of drivetrain friction at stake is quite small, likely considerably less than 1W.

I suspect the symptom of slipping could be mitigated for a while by increasing chain tension, but it would only be a short-term fix.

Here's a trace of one of your photos highlighting the teeth. See how the grannie ring has nice fat teeth, with a pronounced width and a curve over the top of each tooth? This ring has seen little use and is perfectly serviceable.

The middle ring is quite worn but probably worked well-enough with a worn chain (they tend to wear together. Notice the valley curves between teeth are not even - Compare with the flipped image on the right and they have a definite "handedness" - that is, in these photos the teeth on the middle ring are leaning "backward"

The big ring has developed short "flats" between the curve and the teeth. This is where your chain is slipping off because its too low.

ANSWER If you increase chain tension, it might help hold the chain's roller in the valley curve, but there's not enough metal left in the shoulders of the tooth to really make much difference.

The cost of replacement derailleur springs would be better spent on a new chainring.