Yes you can
I am aware of this tweet and I think its wrong.
The rules say:
Movement and Position
On your turn, you can move a distance up to your speed. You can use as much or as little of your speed as you like on your turn, following the rules here.
Breaking Up Your Move
You can break up your movement on your turn, using some of your speed before and after your action. For example, if you have a speed of 30 feet, you can move 10 feet, take your action, and then move 20 feet.
Moving Between Attacks
If you take an action that includes more than one weapon attack, you can break up your movement even further by moving between those attacks. For example, a fighter who can make two attacks with the Extra Attack feature and who has a speed of 25 feet could move 10 feet, make an attack, move 15 feet, and then attack again.
Moving Around Other Creatures
Whether a creature is a friend or an enemy, you can't willingly end your move in its space.
The rules permit you to insert your action into your movement anywhere and prohibit you from willingly finishing your movement in another creature's space. They are silent on using your action while within another creature's space so we should adopt this tweet:
Beware of claims that a rule does something mentioned nowhere in that rule or elsewhere in the core books. There aren't secret rules.
Presumably, we should beware of claims by the author of both tweets where Sage Advice continues to remain silent on the matter.