KTX stopped trains from Incheon Airport as of last month. So now you have to take AREX Express or all stop train to Seoul Station, then take KTX from there.

Its about 50-70 minutes to Seoul Station depending which AREX train you take. Express train is every 20 minutes, so even thought it “saves time” you might be waiting around for it thus defeating any advantage.

There are trains to Busan that depart every 15-20 minutes. At peak times, like early morning, after work, Sat AM, Sun PM trains do sell out. You can always buy in advance and even get a refund after departure minus like a few thousand won (maybe 10% fee after departure?) if you find yourself late for your train.