Ranger has an advanced move 'A Safe Place'. The trigger is 'when you set watch for the night'.

Most of the other players are much more experienced at fantasy setting routines (setting watches, marching order, etc.) and I expect that they will simply slip right into that without consulting anyone (the party leader likely calling duties).

So I sort of interrupt and say "Um. I'm really good at setting watch; can I do it?" or some more heroic way of saying so.

If done in-character, they may or may not defer.

Do I simply make it known OOC that I actually have an advantage at this?

Or perhaps that is part of the collaborative table discussion, so that they'll already know this when sitting down at the table?

Maybe I could hint to one of my bonds, who knows me already, that they've seen me excel at this, so it doesn't look like I'm begging (either as player or as character).

Or am I overthinking this?

"Y'all know me. Know how I earn a livin'."

(chalkboard scratch optional)

They do all know you. They've written you in their bonds, and if not that, then at least you've written them in yours. You've guided one of them through the wild before and they owe you. You're teaching one of them how to survive in the wild.

Your character sheet is also not some secret from everyone. The GM's spoken openly with you about it in front of the whole table, and if you haven't leveled up while everyone is there - if you created a character at a higher level - you've gone over the advanced moves you picked as part of your introduction as a character.

And if someone forgets? "Address the characters, not the players" is only there for the GM, in the GM's chapter. Players can talk to each other however they'd like. "If I set the watch, everybody takes +1 to take watch" is a completely legitimate thing to say.

You're overthinking this, just tell them OOC, applying the Murky Mirror

I basically agree with Glazius's answer, but it's worth knowing about the concept of the Murky Mirror as a tool for making roleplaying easier. This obviously depends a bit on your group dynamic. If OC chatter at your table is heavily frowned upon, then I guess this solution isn't appropriate, but I'm a big fan of the Murky Mirror concept, introduced by Angry GM.

Presumably your table has had conversations along the lines of "So my guy's a ranger, he's dead good at bows and stuff", "Cool! I've made a paladin, she can take like 10 billion damage before she falls over". You then act on this information in combat, by putting the paladin in front of the ranger so that she takes damage whilst he pew pews. But hold on! Your characters don't know that! You had that conversation out of character! You can't act IC based on OC knowledge!

Except your characters are probably all experienced adventurers. They know what other experienced adventurers look like. When the Paladin says "my character is really tanky", your character is looking at the imposing warrior striding confidently next to them, noticing the polished but dented armour, the network of scars on their face, the bent nose that's been broken at least seven times, and the stern, hardened grimace, and thinking to themselves "well, they can probably take a punch far better than I can...". It's just that describing that little vignette at the table for every facet of every character would be a bit boring, so we just abstract it away when somone says "I've got X hitpoints".

So next time you set up camp, you can say "by the way, my guy gets a bonus if he's the one who sets up watch, mind if I do it?". That sentence is the vignette in which your characters are all unpacking their bedrolls and making the fire, and maybe your ranger talks about how they've walked these paths before. They recognise the tracks, know what creatures lurk in the forests, and which ones you should worry about. If you want to actually narrate that scene once you've communicated the mechanic, it'd be some cool flavour and I don't think anyone would mind. You shouldn't, though, feel as though it's "Bad Roleplaying" to briefly tell people what's on the sheet in front of you, especially if it helps the party operate better.

_{(Small note: there are a couple of tabletop systems where it is not appropriate to share information on your character sheet because your characters are expected to keep secrets from each other - Call of Cthulu and Paranoia for example. Your GM should tell you if you're playing one of those games. A good rule of thumb is that if you're spending a lot of time passing notes to the GM and back, you probably want to keep that character sheet hidden)}