Apols for the copy and paste (and the unsolicited bump), but I have just written a fairly long reply on a different laundry thread, saw your thread suggested underneath it, and saw you didn't get many answers, but we get exactly the same issue, especially with darker clothing - I have now solved it, and I suspect the issue is that we tend to wear things multiple times before washing and with the darker items, they probably get worn even more often as they are less likely to show marks, so over time they just get insufficiently washed again and again and have a load of build up which needs to be removed.
First - go back to basics with the products and process.
Long/full washes - no quick wash. Generally choose the standard Cottons 40 degree wash cycle (the most basic one on the machine). Don't overfill - aim for about 2/3 full. Make sure there is about a handspan of space (closed fingers OK) between the top of the clothing and the top of the drum.
Trial and error with different washing powders/pods. In the UK I used to get good results with Bold 2 in 1 Lavender, but this was about 13 years ago (I live abroad now). Most machines work best if you put the powder directly in the drum in one of those astronaut hat things (they will usually send you one if you go on the website of any liquid wash detergent). Follow dosing instructions on the box for your load size and water hardness - you may need to look this up.
Try first to get the clean smell with just white vinegar/dettol laundry sanitiser type thing in the fabric softener compartment, without scented products or booster type things. You can add these back later on but try to get a fresh smell without them, otherwise you're just covering it up. I've never noticed any difference in softness at all with/without softener. The only result I notice is a stronger scent.
Second - check whether your clothes have build up
After a wash cycle, smell the wash load. If it doesn't smell fresh and clean then some of the clothes probably haven't been sufficiently cleaned. IME this can happen if you've been overly packing the machine, or not choosing the right wash cycle for the level of wear, overusing detergent or drying clothes too slowly over a long period of time. If you wear clothes multiple times before washing them, most machines have a button to boost the cleaning cycle, which adds either some extra water, extra agitation or both (often called something like "intensive" or "extra"), or use the amount of detergent suggested for medium soil - it's still more economical than washing them after one wear. You can literally just wash the entire cycle over again, it often takes about 2-3 washes to clear up, but if you feel like particular clothes have more of an issue, you could sit there and smell each item individually (I have done this!!) and only re-wash the specific items which consistently don't get the fresh smell.
For anything where the smell doesn't clear even with multiple washes, try sticking it in a smaller load, at a higher temperature and/or with more washing powder and/or the "intensive" button etc. I get a particular issue with my tops as the underarms hold onto a stale sort of smell, not even BO but something else, perhaps deodorant. Anyway an acid applied directly to the armpit area can help with this - white vinegar again or there's usually a spray in the stain remover aisle for sweat and deodorant, which works well too. If this isn't enough, save the offending articles and throw them into the next 60C wash - this seems to do the trick and it's very rare I find clothes are damaged by this wash if it's occasional - obviously not for things which are delicate but it might be worth a last ditch effort if you'd otherwise throw the item away.
For the black t-shirts and kids' jogging bottoms I find they tend to have a smell which I can only describe as being like pasta water. It's not bad exactly but it's just not really clean either and it prevents the clothing from taking on the scent of the washing powder, which is what I like.
Soda crystals will have a stronger effect than bicarbonate of soda, but there's no point putting soda crystals and vinegar in the same wash cycle unless the vinegar is held until the end e.g. in fabric softener compartment.
It's normal for there to be water in the conditioner drawer and not a problem. It's how the machine pushes the contents of that drawer out at the right time and not too early. You might want to leave the drawer slightly open as well as the washing machine door open between cycles so it can dry out.