any reason you can't place u4 on top , let's say near u2 or between connectors?
would help with all those traces cutting the copper fill on bottom
can you replace c2 with ceramic capacitor (or several in parallel) or a surface mount capacitor?
This and battery are the only through hole parts.
if possible consider movng the battery holder below chip, near connectors.
Would allow you to shift the main chip up and shorten and reduce all those traces going to left i/o pins leaving you loads of room to move at least the capacitors for oscillator on top.
move RESET button on left side above the io pins ?
move 3.3v and ground on left as well so you don't need that long trace on bottom going to both sides of board.
Maybe if possible, have the whole row of pins a few mm to the right, leaving more room for that 3.3v trace to go between edge of board and pins.
are those r5,r6,r8 same value? maybe you can replace with single part with multiple resistors in parallel to reduce space used.
Here's a very crude mockup i made in ms paint, shifting some components a bit

and loads of room on back side for ceramic capacitors and resistors under where u3 used to be and under the battery holder... your only issue is gonna be where the 3v from battery lands right in the center of the board, but you can route that trace to where it's needed easily
you could also get those 4 traces on the bottom going down to the connector closer together so they don't break that ground fill so much