Yes, you are correct. But in the video, the speaker references the M8 galaxy, not the universe.
This is just the section that discusses Stars vs Trees

https://youtu.be/8FxTgaHnbXE?t=1422&si=qSNBFNH7C8tbvehU

Transcript:
Which do you think is greater, the number of stars in the galaxy or the number of trees on Earth?
It's a bit of a strange question, but most people believe there's an obvious answer. The M8 Galaxy is over a 100,000 light years wide and a thousand light years tall and Earth, is just Earth. Surely there must be more stars than trees, right? That's the more commonly guessed of the two answers but it turns out that's incorrect. At least we're pretty sure it's incorrect. According to our best estimates, there are between 100 and 400 billion stars in our galaxy while there are three trillion trees here on Earth. Of course these are just estimates using sample sizes and extrapolation and whatnot. Nobody has time to sit down and count every star or tree so it's certainly possible the numbers are a little off. However, since the estimates state that there is an order of magnitude more trees than Stars, it's unlikely that the margin of error in the estimates would swing the numbers back in the favor of stars.

So based on that - I interpret the conversation to be about trees vs a single galaxy.

Yes, you are correct. But in the video, the speaker references the M8 galaxy, not the universe.
This is just the section that discusses Stars vs Trees

https://youtu.be/8FxTgaHnbXE?t=1422&si=qSNBFNH7C8tbvehU

Transcript:
Which do you think is greater, the number of stars in the galaxy or the number of trees on Earth?
It's a bit of a strange question, but most people believe there's an obvious answer. The M8 Galaxy is over a 100,000 light years wide and a thousand light years tall and Earth, is just Earth. Surely there must be more stars than trees, right? That's the more commonly guessed of the two answers but it turns out that's incorrect. At least we're pretty sure it's incorrect. According to our best estimates, there are between 100 and 400 billion stars in our galaxy while there are three trillion trees here on Earth. Of course these are just estimates using sample sizes and extrapolation and whatnot. Nobody has time to sit down and count every star or tree so it's certainly possible the numbers are a little off. However, since the estimates state that there is an order of magnitude more trees than Stars, it's unlikely that the margin of error in the estimates would swing the numbers back in the favor of stars.

So based on that - I interpret the conversation to be about trees vs a single galaxy.

It seems that our universe is expanding faster than the speed of light, and that imposes several restrictions on us. If we were able to travel a certain distance from earth, we would never be able to return because of the rapid expansion. Also, distant light will never reach us because it is moving away from us too fast.

When the Milky Way and the Andromeda Galaxy collide in millions of years, not one of the billions of stars will collide with another. A spaceship traveling at the speed of light could travel indefinitely in a straight line and not crash into anything. These are two results of the universe being incomprehensively large.

Unrelated, but interesting:
When you shuffle a deck of cards, you will get a result that has never been gotten before.
There are more trees on earth than stars in the universe.

This guy is interesting - https://www.youtube.com/watch?v=8FxTgaHnbXE

It seems that our universe is expanding faster than the speed of light, and that imposes several restrictions on us. If we were able to travel a certain distance from earth, we would never be able to return because of the rapid expansion. Also, distant light will never reach us because it is moving away from us too fast.

When the Milky Way and the Andromeda Galaxy collide in millions of years, not one of the billions of stars will collide with another. A spaceship traveling at the speed of light could travel indefinitely in a straight line and not crash into anything. These are two results of the universe being incomprehensively large.

Unrelated, but interesting:
When you shuffle a deck of cards, you will get a result that has never been gotten before.
There are more trees on earth than stars in the universe.

This guy is interesting - https://www.youtube.com/watch?v=8FxTgaHnbXE