Shocker
Sure they can't, but they can prohibit them from playing games for their new team if they don't get through the administrative process. So if the option is extending until the end of the prolonged season, or not playing at all until you're allowed to for your new club, players might think twice about extending...
UEFA's comments about "30 June meaning the end of a season" is too big of a leap legally speaking, contracts need to be executed in good faith yes but interpretation only comes into play if the terms are unclear or open to interpretation. An ending date of June 30 is as clear as it gets.