My plan would be to use the salary information available from spotrac.com as it provides both the year-by-year salary as well as contract information like arbitration status, free agency status, and even options (club options, player options, mutual options) so that there is one source that everyone can readily access. Before the start of the draft, I will transfer that data into a spreadsheet that can be referenced as part of draft preparation. Of course, that data can change here and there and the spreadsheet would be updated from time to time through the end of the season. I would presume that any salary listed for the current season would remain static from the opening of the draft to the end of the season. Presumptions would be made for any players not listed on that website.
Just as in MLB, the salary is guaranteed. So the standard answer would be that each team would be fully responsible for those salaries unless the player is traded to another team which would assume those salaries going forward. Simply dropping a player would not free up the $. I have toyed with the idea of a partial return in cases of players who are placed on the 60-Day DL - like an insurance policy.
Naturally, there would be supplemental opportunities to add players and those additions' salaries would be prorated. The frequency is something that would be up for discussion as I don't think there is a definitive best practice. Injuries happen throughout the year, after all.
As for the Ohtani example: he is listed with a salary of $70 million per year for the next 10 years. For Year 1, the owner's immediate responsibility is his Year 1 salary. This brings up a question I have already considered: should the salary cap be adjusted to accommodate an outlier like Ohtani? Adjusting the cap for one player makes it less meaningful. As it stands, Ohtani's salary would absorb about 37% of a team's cap, making it a difficult pill to swallow. But, that is the kind of choice a cap meant to create. The cap, as is, does not preclude a team from drafting him. But it does limit that team's flexibility to build around him.
Whew ... that's deeper than I was hoping to go. I'm happy to listen to feedback. Just send me an email (rsa95525@gmail.com)