That site is confusing. I can't make heads or tails of it either. I would recommend:
https://basketball.realgm.com/nba/draft/future_drafts/detailed
Which makes a lot more sense but doesn't list picks that *haven't* been traded. So, basically, assume you keep any future picks unless they're listed in the second "outgoing" column.
The basic answer right now is that we hold all our own first rounders (and nobody else's), we hold all of our second rounders except 2024, and we have incoming seconds in 2022 (worse of Detroit/Chicago), 2024 (Portland), and 2025 (Portland). There's a chance that we pick up a 55-60 2022 2nd, and that we lose our own "highly protected" (unspecified) 2022 2nd, but those are likely not changing hands.