In the screenshot in the Original Post, to create your background is quasi-official. The textbox says.
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BACKGROUNDS AND SPECIES FROM OLDER BOOKS
Backgrounds in older D&D books dont include ability score adjustments. If your using a background from an older book, adjust your ability scores by increasing one score by 2 and a different score by 1, or increase three scores by 1. None of these increases can raise a score above 20. ...
Also if the background you choose doesnt provide a feat, you gain an Origin feat of your choice.
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On the one hand, using an earlier background is an "if". On the other hand, it offers official advice as a normal option that players might do. A custom background is something like 2024 variant rule. The 2024 rules adjust the custom background from the 2014 Players Handbook as follows.
2014 Customizing a Background
• choose two skills
• choose two tool proficiencies
• choose personality
2024 Using a background from an earlier book
• adjust ability scores (+2 any and +1 any other, or +1 any three)
• choose origin feat
This resulting custom background is slightly more powerful than a 2024 default background because of the extra tool proficiency. Perhaps it is a reward for players who put thought into their background. Meanwhile, the 2014 personality can correlate with the 2024 personalities relating to the abilities of a background.
I am ok with this custom background being a variant rule that implies DM permission, because the DM might need to adjust the setting to accommodate a certain custom background. For example, if the custom background is a Soldier who proficient with both an Air Vehicle and a Water Vehicle, the DM might want to think of a specific military unit at a specific location where this would make sense. Meanwhile, the player and the DM should be coordinating the background with each other anyway. The DM setting description can inspire the player character concept − and viceversa.
The player is responsible for the character. The DM is responsible for the setting. The background is where these responsibilities overlap.