I don't know if there's an official recommendation. I used to use Arctic Silver, but I'm sure any reputable brand would work.

So this is my third time having to remove the battery on this device (once for the screen, once for the battery, and now for the charging assembly). Dropping a little high-percentage IPA into the left side of the battery worked like a charm! The tabs immediately tore, as they always do, but after letting the IPA sit for 30 seconds or so, prying the battery up from the left with a pick was super easy. Just let everything dry before applying the new adhesive. Maybe it was just that my adhesive had only been sitting for like six months.

Strongly suggest that before removing this last bit of adhesive, flip the back cover over and turn the phone on to confirm operation! If it doesn't work, this is the last chance to debug/fix it before the adhesive makes it much more difficult to do so.

Solid guide, though I wonder why some of the order differs from the others Pixel 3 guides, especially with the battery. Why not take it out immediately? Trickiest part is the initial opening - take your time, multiple iOpener passes, and come at the seam at an angle with the pick - and the earpiece-motherboard situation - the earpiece is stuck on with a strong adhesive, so trying to pry it up prior to removing the motherboard can be disastrous (for the earpiece). I found the magnetic project mat that iFixIt sells to be very helpful. Make sure to get a new speaker gasket as well, and new battery adhesive, or use Tesa tape. The standoff driver was bonus, but far from necessary. Also! Get some of the graphite sheeting that iFixIt sells for the Pixel 6, 7, or 8 to replace the stuff you inevitably tear through when removing the battery. Just cut it to size, pretty sure it's the same (or similar but upgraded) stuff. Good luck! Definitely block out a solid four or five hours for this - reduce time pressures!

For re-assembly, I think that, for the double-holed clip, the large clip is held on by the 1.9 mm screw in step 36, whereas the smaller hole drops down to be held in by the 4.1mm screw in step 16.

Agreed - see my comment two steps above (#57). Probably better to remove it earlier too to reduce chance of damage.

Personally, I feel that the better path is removing the battery earlier (reduces the chance of accidental puncture with tools; basically as soon as is feasible to do so) and replacing it later in the reverse process (to make sure it's positioned correctly before applying the adhesive that's tricky to remove).

When re-installing, do this after the motherboard. Removes the difficulty of getting the cable back over the top, and it's just adhesive-connected so it's easy to push into place. Gently.

If you're going to remove the earpiece (with the orange semicircular flex cable) at this point as suggested by Ray, note that the adhesive holding it to the frame is, well, right at the frame. I say this to note that it's lower (in depth) than it seems, and when I tried it, I accidentally popped the metal earpiece cap off entirely, which encases the earpiece, but did not remove the earpiece adhesive at all. So if you're going to try and remove the earpiece first, I suggest heating that area first (iOpener good here) to loosen the adhesive, and really digging in there.

Alternatively, just be careful with the cable. After breaking the earpiece, I took the motherboard out, and the cable barely got in the way at all.

If you need a replacement earpiece (like I did) and are sad to discover that iFixIt doesn't sell them (like I am), you can get them on eBay relatively easily these days.

To expand on Ray's comment, the light blue box in the second image was disconnected previously (it's the display cable in step 32). The press-fit connector that should be highlighted is in the first figure, lower-right portion of the screen above the silver-colored box with the hole in the upper-left corner. Oddly enough, you can't see the disconnected cable in this figure (it's just gone), but it's shown in step 33 with an orange flex cable underneath the thumb.