Veneer furniture wasn't built with refinishing in mind so you are correct in using caution to avoid sanding through. You are also correct that living with a few imperfections is wiser or i should say practical than going for perfection. Something with that cloud in finish suggests wax has been applied at some point,or worse pledge or other silicone product. It would have been best wiping it down with wax/silicone remover before sanding but better now than not. Since oil has penetrated all the way through veneer there is not a point of no return ( like happens if applying varnish) if you use oil for new finish. With that in mind I'd go to 120 grit and see how it looks. If you aren't pleased go back over it with 100 then repeat 120. I'd like you to try a technique I've used for decades ,there's nothing to loose and you might become a convert for future projects involving oil finish or worn finishes. Wet surface with your selected oil then sand with 150 wet or dry paper. Use just enough oil to create a slurry, add oil as you go if needed. Once surface is coved in slurry wipe it off to see how you like finish. Go at it again using 180 or 220. Each step in grit exposes detail that wasn't visible before. Some fine woods have detail that doen't fully appear until 400 but the pay off is less for others. Let me know what you think about this technique,esp ease of doing and level of appearance. You might try this to renew items not badly worn but not looking their best. If the wood features pop people tend to overlook imprefections such as scratches,dents and missing wood.

You definitely need to sand more, but put away the heavy grit and use 120. No need to get every scratch out but you can see now that there is a lot of finish left. I would use tongue oil when your finished.