My background: I am married to a very introverted person, and I have had to explain his disappearing act when he needs to go recharge. I understand the reluctance of explaining what you're doing and why you need to recharge/rest.
How can I approach this issue politely without hurting feelings and harming my relationships?
I would like to have a way to hint them/ give signals when I start getting tired and need a break from the conversation, that they would understand and don't feel bad about.
If you interact with these people on a daily basis:
Let them know early on that you are an introvert and need time to "recharge" occasionally, and do not mean any insult to them when you leave the conversation. It helps here when you know them, they will be familiar with you leaving to recharge, and think nothing of it.
When with friends, tell someone that you need to recharge/rest, and if anyone asks for you while you do whatever you need to recover, that friend can "cover" for you, and simply say "cinnamon has gone to recharge, they'll be back sometime, be patient please."
When you feel the need to recharge, let them know using "I/me" statements to avoid putting blame on the other person.
I need to take a few moments to recharge, I would love to continue this conversation later, is that okay?
If you do not interact with these people on a daily basis (acquaintances):
Same thing applies here- Let them know early on that you are an introvert and need time to "recharge" occasionally, and do not mean any insult to them when you leave the conversation.
This step may be harder when you're not around friends, but it shouldn't stop you. If there is one person around you that you feel comfortable with, maybe not necessarily a friend but a trustworthy person- you can tell them if anyone asks for you that you have gone to recharge and you'll be back sometime.
When you get tired, find a good time in the conversation to say that you need a break, and you need to recharge.
I need to take a few moments to recharge/rest, I would love to continue this conversation later, if that's okay with you?
- Maybe then you can exchange phone/text numbers if you want to continue at a later time if the person is not available later in person.
The overall goal here is to have you clearly and succinctly state that it is YOU, not THEM that needs a break, and if they have a problem with that, it is not your responsibility to entertain them or keep talking with them. The best way is to not make excuses, and just state what you need and express desire to continue the conversation.
Expressing the desire to continue the conversation at a later time politely informs them that you are not trying to get away from them because they are talking, but that you are tired.
I need a few moments to recharge/rest. May we continue this conversation later/at a better time over a meal, next day, over text, in a game, etc...
There are so many possible modes and locations of communication!
One of your concerns:
Most extroverts don't understand that feeling and either feel personally attacked/unwelcome or can't take the issue seriously and say stuff like "come on, it's not that bad, you have to get used to that". (These are my common experiences).
Repeat what you need to say to tell them you need time to rest, and that they can continue the conversation later at a better time. If they keep insisting, maybe go to a trusted person or a friend to let them know that this person won't let you go rest/recharge/recover.