I've tested your request. It worked.

page    1
total_results   381271
total_pages 19064
results 
0   
vote_count  0
id  465559
video   false
vote_average    0
title   "The Zero Century: Maetel"
popularity  1.014031
poster_path "/oFbrPffgM94psqkdxiXMTlCvCtU.jpg"
original_language   "ja"
original_title  "零世紀 メーテル"
genre_ids   
0   878
1   16
backdrop_path   "/19URihLRPW7r2sFSvjpFZDKfrAM.jpg"
adult   false
overview    "The story of Princess Maetel and how she came to start her timeless train trip on the Galaxy Express 999."
release_date    "2026-01-01"
1   
vote_count  0
id  417773
video   false
vote_average    0

Maybe your Key is in trouble.
Verify that it is valid. Go to your profile and see in API.

Edit: &include_video=false

page    1
total_results   364483
total_pages 18225
results 
0   
vote_count  0
id  465559

key valid, and request work, but I don`t get video video: false although I set include_video=true

What do you mean by Video?
The trailer? Or watch the movie?
If it is to watch the movie, impossible.
TMDb has no link to watch movie.

trailer

The function of this parameter Video is not to request trailer.
The TMDb database can be divided into two parts: Movies and TV Show.
In the Movies category, there is the division between what is a movie, with a movie premiere, ticket sales, etc ...,
and what is classified as video, things released only on DVD or Bluray, or a rock show , or jazz.
So, the video: true parameter only specifies that you want to be included in your search results, such shows, concerts, etc ...
If you look at the two tests I did, you'll see a small difference in the quantities.

&include_video=true  
page    1
total_results   381271
total_pages 19064  

&include_video=false
page    1
total_results   364483
total_pages 18225  

To receive the link from the trailers, I think only by searching with the ID of each movie.

sorry, my fail. Thx.