IMO that is a lot & needs to be dealt with. Pulling side to side like that is a good way to get a feel for slack especially if you have an indicator mounted to quantify what you are suggesting is 0.100" on both X & Y axis. Having float on both axis is double the fun because it is free to roam in an area as opposed to just a line as if only one axis had wear & the other locked. However its those temporary unlock transition moments when you set up for another traverse (just like you described) where the surprise can bite you.
Most people phrase this effect it in terms of dial backlash, its really the same thing. Its nice if you have DRO for following test but can do as easily with DTI in spindle against a reference block edge.
- dial in-feed direction only, say 3 turns so leadscrew backlash is fully taken up, don't reverse dial direction during process
- stop dial on handy dial reference like zero
- zero the DRO/DTI at this exact same spot
- slowly reverse handwheel until DRO/DTI moves off its null position, make note of how much handwheel dial movement has occurred (yours might be close to 0.100")
Video shows the ballpark shortcut without a DTI/DRO but I like the reference method more because its more repeatable & precise for what I also recommend: Repeat this at different spots on your leadscrew like 1/3, 1/2, 2/3 table displacement positions. You may find the wear is in concentrated in the middle most used area. Good to know but doesn't usually change the strategy or remedy if excessive wear is the issue. Next you need to know if you can dial this out acceptable with leadscrew nut anti-backlash adjustment as per video, so try that first.
If the available anti-backlash has been bottomed out by years of increased adjustment, then you need to pull LS assembly to examine. If you are lucky the majority wear will be confined to the brass/bronze nut (=sacrificial wear material). But if its also the LS threads, not at all unheard of, its new leadscrew time & usually do the nut as well so they are a happy low tolerance couple. I should have mentioned the dovetail gib adjustment also factors in this, but not really. Its more a tightness of fit to dovetails & angular table float. Some people crank up the dovetail tightness so it feels stiffer & floats less, but you are not fooling the leadscrew wear if that's the issue. Worse yet table can get sticky when too tight & the cutting action can easily kick the table through its float range & nasty surprise time. Wrecked part, broke tool etc. But you If you have that adjusted the gibs OK, suspect the focus is on lead screw / nut.
I have not exhaustively checked this out. I'm still qualifying the mill before deciding which one to keep. But yes, if I keep it, the Bridgeport may need new nuts and screws. The screws themselves are both visibly worn more in the center than the ends and the backlash is correspondingly worse in the middle. (see my thread "New to me Bridgeport Mill").
I have not tried adjusting them to get some out. I had planned to do a little milling first to test the mills bones out before doing anything like that. Not big jobs - just little ones like making a mill stop and vice clamps. If I decide to keep it, that will be among the first major repair jobs I do. In fact I may even install new lead screws and nuts.
I didn't really expect to break an end mill on my first job though so maybe I should rethink that......