Doug's first paragraph is what I was going to say.
Regarding the dull look after re-sanding- that does not surprise me, it is what can be expected with just one oil application. The wood was probably just as dull before that first oil coat, even if sanded to fine grits. The first coats of straight oil, raw or polymerized, will always soak right in, accentuating the grain colors, but not doing anything for the surface appearance. Depending on the wood, straight oil will start to remain more on the surface around a 3rd or 4th application, I've found, characterized by blotchy penetration. If I'm finishing with only oil, that is when I know for sure to not bother applying further coats. Further coats will remain on the surface more with each coat, and do little inside the wood. You can use this to your advantage with the extra coats, lightly wiping down each of them to avoid blotchy looking patches, but now the oil at the very surface will in itself cure into a top coat. Nowhere as tough as resin-containing oil (aka varnish), and without any obvious, unnatural reflective sheen, but the coats should look better as you add more, but it takes lots of time to cure all those coats.
For me- one coat of oil pops the grain, but looks flat/dull, as you observed. A second coat may help the first coat with the grain appearance a bit, but only improves the dull wood surface appearance a little bit. A third coat, it won't penetrate too much more, but after that coat is buffed with a soft cloth or paper towel, the overall appearance is looking pretty good, no longer dull, but no obvious plastic surface layer, either. This is where I normally stop, and I'm using polymerized oil myself (Tried and True products). Most times with dense woods, I'll stop after 2 coats. Rock hard, oily woods like cocobolo, you get to apply one very light coat of straight oil and it's not accepting any more after that, and you have to watch for bleeding oil for a few days, or longer, wiping it down well when found. (Watch what the wood is trying to tell you.)
I'm not looking for obvious surface films myself, but I could keep going with 4th, 5th, or more oil coats to start creating a surface film low sheen, but I need to be careful of those blotchy patches where the oil just is not soaking in anymore. I don't watch those blotches to cure on the surface, because they look awful.
I'd give plenty of time for the straight oil coats to cure before a final top coat of wipe on varnish (such as Watco, Waterlox, homemade wiping varnish concoctions, etc.). The test I use for checking cured oil finishes is this- wash and dry your hands well to remove skin oils. Look at the surface of the wood carefully under good light, make sure it is dry on the surface and not looking or feeling oily. Then pinch the wood firmly and hold that pinch for 30-60 seconds. Let go and immediately look at the surfaces where your fingertips were pinching, under good light. Move it around under the light. Do you see oily fingerprints, obvious or even the slightest hint of them? Then the oil has not fully cured. (Wipe off the oily fingerprints so they don't cure on the surface.) Do this in a patch of side grain wood and end grain wood, the end grain may show oily fingerprints for a longer duration, may need more days of curing. Be patient and try this every couple days until you get to the point of no oily fingerprints for several days running. Now your oil finish is likely fully cured, and if you've been watching a calendar, you'll see that maybe a week, or three or so, had gone by. Patience with oils, patience... The more coats of oil, they longer the curing process, maybe a full month.
Too much time? Try one coat of oil, applied and wiped/buffed on the lathe, and apply no more. Remove and set on a wire rack elevated off the table part of an inch so air gets all around it. Warm air, above 70. Do the finger pinch test, it'll probably show dry with a week. Then continue your finishing process as desired with the wipe on varnish products, building as much as you please.
I've posted in recent months about a couple version of warming/curing kilns to help speed the oil curing process. Just don't go crazy with the heat.
Here's an idea for a small oil finish curing kiln. Nothing too new here, but rather than the incandescent bulb heat source of the past, he uses a reptile cage heating element screwed into a lamp socket as the heat source. He's not using this kiln to dry wet wood (you could, but his carved wood is already at equilibrium by this point), rather he uses it for curing pure penetration oils like tung and linseed. Maybe someone here will find the concept useful.
https://davidffisher.com/2024/05/04/nine-in-the-new-kiln/
Dave Fisher is a renowned carver of bowls and utensils, he creates...