New player here. I just finished the campaign and hit the level 20 cap. What to do?

Hi all,

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I bought just the base Destiny 2 game a couple of weeks ago to try it out and I ended up really liking it. Just last night I finished the campaign (credits rolled) and hit the level 20 cap. What should I do now? Do I buy the Forsaken expansion? Also I noticed that the level progress bar is still going up when I get exp despite being at lvl 20, what does that mean?

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Thanks in advance,