Create an intake queue and direct them to that. Service it on a stated SLA that you decide. Do not respond directly to ad hoc requests (outside of perhaps company wide campaigns that you are in risk of missing).
This is all incredibly difficult in a large company.
The intake queues suck because _some_ teams respond to Service Now and some don't. Like, you'll have a pretty easy task which requires stuff from 3 teams, 1 you put in the ticket and they do it same day, the other sits there and never gets picked up, for the third you can't even figure out which team is supposed to do it let alone how you would contact them. So, the hunt begins, and this requires talking to actual humans. Sometimes there are 2 or more teams who could do your thing in different ways but none of them want to.
This is made worse by some parts of the company on webex, some on slack, some only available on teams, some teams responsive to email and others not really etc.
The only thing that makes the whole engine work is an informal network of people that trust each other who glue the whole thing together behind the scenes.
The OP's problem is that large company communication is universally dysfunctional and the "glue" network between them and the people who need things from them is not strong enough. It helps to have a strong informal networker in the reporting chain. This is usually some kind of team lead and everyone accepts that their productivity will be destroyed because "everyone knows who they are" and contacts them out of the blue with their wacky requests. They should then prioritise and route appropriately.
If leaders are not amenable or functional in this way they get routed around and "person you contact to get things done" increasingly diverges from formal leadership.
IMHO, a keen eye for how the organisation actually functions, careful relationship management and knowing which levers and channels to use to get things done are the skills of a 10x person in enterprise.
Your response is exactly why artificial boundaries should be set up. Most of these requests will not be important and they should either be dissuaded entirely or dealt with much later. The ones that are important (note: very infrequent) will be in the hands of someone capable of navigating internal politics despite the existence of a "stop bothering me" canned response.
Every team I work with (very large company) leverages this approach, their productivity would be Nil if they left a direct channel wide open. Back channels exist only where they should exist.
The intake queues suck because _some_ teams respond to Service Now and some don't. Like, you'll have a pretty easy task which requires stuff from 3 teams, 1 you put in the ticket and they do it same day, the other sits there and never gets picked up, for the third you can't even figure out which team is supposed to do it let alone how you would contact them. So, the hunt begins, and this requires talking to actual humans. Sometimes there are 2 or more teams who could do your thing in different ways but none of them want to.
This is made worse by some parts of the company on webex, some on slack, some only available on teams, some teams responsive to email and others not really etc.
The only thing that makes the whole engine work is an informal network of people that trust each other who glue the whole thing together behind the scenes.
The OP's problem is that large company communication is universally dysfunctional and the "glue" network between them and the people who need things from them is not strong enough. It helps to have a strong informal networker in the reporting chain. This is usually some kind of team lead and everyone accepts that their productivity will be destroyed because "everyone knows who they are" and contacts them out of the blue with their wacky requests. They should then prioritise and route appropriately.
If leaders are not amenable or functional in this way they get routed around and "person you contact to get things done" increasingly diverges from formal leadership.
IMHO, a keen eye for how the organisation actually functions, careful relationship management and knowing which levers and channels to use to get things done are the skills of a 10x person in enterprise.