how to SEE/notice "invisible" threats better

cct=checks captures threats. simply list all your opponents captures and your reply before each move. I do this as part of my tactics training. Be patient. It takes time for study to work into game play. For me it has taken 6 months for cct to become more natural and habitual. And play longer time controls of course.

Play 30 minute games. Whenever you make a move, check whether you left a piece or even a square undefended, especially pawn moves because they neutralize pieces. You make a move with a pawn and the next thing you see is a knight forking your king and rook because that pawn you moved was defending a potential square for the opponent's knight. Look at the position of your pieces. Is your Queen positioned on the same diagonal as your king? Might get pinned/skewered. Always ask why your enemy made that move. If there is a threat, prepare to defend or counterattack. If none, then check if your opponent left something undefended and punish.