Do you have an R or a GS? It matters.
If you have an R, I believe the parts you need should be an Adjusting Plate (63121600288) ($11.89) and a Fillister-Head Screw - M6X20-8.8-Znniv (11118557331) ($3.35).
If you have a GS, it's more complicated because the parts diagrams do not reflect reality. Everything below here applies only to a GS.
The detail below should enable your dealer to work this out with BMW. Let us know what happens. If your dealer is still unable to get what you need based on this, let me know and I'll try with my dealer.
I happened to have the front end of my 2022 G310GS fully disassembled at the moment. There are four parts associated with adjusting the headlight. These parts are shown assembled in the first picture below and disassembled in the second picture below.
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The first part below is a "C-Clip Nut, Self-Locking - M6". The second part below is not shown or named in the parts diagrams for my 2022 G310GS (provided below), so lets call it the "Lower Headlight and Headlight Adjuster Mount" because, on my 2022 G310GS, the bottom of the headlight is mounted to this piece via the holes on each side of this mount and the Headlight Adjuster mounts through to the center hole of this mount. The third part below is also not shown or named in the parts diagrams for my 2022 G310GS, so lets call it the "Adjusting Plate and Cylinder". I'm calling it this because the parts diagram for my 2022 G310GS does show a part that's called the Adjusting Plate which looks like the top flat rectangular section of this part (I think this Adjusting Plate is correct for the G310R, but not the GS). The fourth part below is a "Hexagon Socket Screw With Flange - M6X50".
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The first picture below is supposed to be the parts diagram for the "Front Panel Carrier" of a 2022 G310GS, but it's actually the front panel carrier of the non-LED G310GS. The second picture below is supposed to be the parts diagram for the "Headlight for 2022 BMW-Motorrad G310GS"; it correctly shows the LED headlight; it correctly shows #6 as "Hexagon Socket Screw With Flange - M6X50"; however, it completely omits the second part above; and it shows an incorrect adjuster part - it shows #7 as an Adjuster Plate when the actual part is a single piece with a plate on top and a cylinder below (what I called the "Adjusting Plate and Cylinder" in the above picture). I think this LED headlight diagram is actually for the G310R, not the GS.
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Below is the actual front panel carrier on my 2022 G310GS. Note that the three circular holes on the left side are not original; I drilled those. On my bike, the "C-Clip Nut, Self-Locking - M6" slides onto the tab at the end of the wood pointer and the "Hexagon Socket Screw With Flange - M6X50" secures what I called the "Adjusting Plate and Cylinder" and what I called the "Lower Headlight and Headlight Adjuster Mount" to the "C-Clip Nut, Self-Locking - M6". It then looks like looks like the assembled parts in the first picture above except that the C-Clip would be on the tab at the end of the wood pointer below.
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Possible (temporary?) fix:
The bolt you lost is a "Hexagon Socket Screw With Flange - M6X50". I'm assuming you also lost what I call the "Adjusting Plate and Cylinder" since it was secured solely by the "Hexagon Socket Screw With Flange - M6X50". The other two parts needed are not secured solely by the missing bolt so you should still have them, the "C-Clip Nut, Self-Locking - M6" and what I call the "Lower Headlight and Headlight Adjuster Mount". This means the only thing you need is what I call the "Adjusting Plate and Cylinder". This is a single piece of what looks like brass with two sections, a rectangular section on top of a cylindrical section. The rectangular section measures 25mm x 15mm x 7-8mm. This 7-8mm dimension is because it's slightly curved along the 15mm side with 7mm in the middle and 8mm on the edges (this curve isn't critical). The cylindrical section is 26mm long with an outer diameter of 14mm; has a 6.5mm hole through the cylinder (the M6 bolt goes through it); and has flat areas on the end so a 10mm wrench can hold this piece while the M6 bolt is tightened.
To make a substitute that should work, make a rectangle =25mm x ~15mm x ~7mm out of hard plastic or metal (=25mm is the important dimension; approximate is fine for the other two), drill a ~6.5mm hole through the center of the 25mm x 15mm face. Then make a ~26mm high stack of M6 washers (or similar) that have an outer diameter of ~14mm. Put the washers on an M6x50 bolt and then put the rectangle piece on the M6x50 bolt. Put some blue thread lock on the end of the bolt. Screw the bolt through the "Lower Headlight and Headlight Adjuster Mount" into the M6 C-Clip. The rectangle fits into a 27mm wide side-to-side space on the underside of the "Lower Headlight and Headlight Adjuster Mount". Keep tightening the bolt until it adjusts the headlight where you want it.
P.S. Have you ever adjusted your headlight adjusting bolt? If not, this should be covered by your warranty. If you have adjusted your headlight adjusting bolt, you might have backed it out too far and then this wouldn't be covered by warranty.
Standing by for questions.