There is something called a disparity of force.
This can allow you to use a higher level of force. Like with multiple attackers, or a major threat, professional fighter etc
Or if you are injured, disabled, in a wheel chair, just had surgery, etc etc
If you are in such a condition that even the unarmed person would cause a "reasonable person" (more on that) to fear for their life or of serious bodily injury.
The problem is many including those on the jury will view fighting like on TV, movies, school, or even boxing and similar sports.
Something not immediately a threat of more than some bruises and hurt pride.
So are unlikely to see an unarmed man attacking another healthy man as a disparity of force.
If those on the jury think your actions are not what they should have been, then you go to prison, or at the minimum become a felon and get probation.
Juries are made up of a lot of people with no experience with violence, soccer moms, housewives, and others with no felony record unable to get out of jury duty. Most people with a lot of life experience seem to get kicked off a jury during the selection process if they are honest.
When serving on jury duty I have been amazed at the naivety of some.
With statements like "well if the police chose to arrest them then they must have done something wrong".
Facing a such a jury tasked with determining if your use of a weapon on an unarmed person was "reasonable" is not something I would recommend.
They are the "reasonable person".
is a broken glass bottle or a club a deadly weapon?
Yes, but if you did not bring it with you then you get bonus points in the eyes of a jury. If it was something you carried for use as a weapon (even in self defense) then its not viewed quite the same, as a spur of the moment improvised self defense out of desperation.
also does the above apply if there are multiple agressors [they encircle/corner you] and you didnt do anything to provoke or escalation the situation?
Multiple aggressors is a disparity of force. That justifies use of a weapon for most "reasonable" people.
However keep in mind they are many witnesses and you are one.
They may say you were the aggressor, and if you pulled a weapon before they even attacked it wouldn't be an unreasonable claim that you were the criminal who pulled a weapon over an argument with one of them.
But if you don't do something you may end up hurt or dead.
So it is best to avoid situations where the aggressors have more friendly witnesses who may lie, or may claim to have seen nothing at all.
Even if you do nothing illegal their united story may make you out to be the problem.