According to the Free Rules 2024:

Parts of a Background

A background includes the following parts.

Ability Scores. A background lists three of your character’s ability scores. Increase one by 2 and another one by 1, or increase all three by 1. None of these increases can raise a score above 20.

Feat. A background gives your character a specified Origin feat (described in chapter 5).

Skill Proficiencies. A background gives your character proficiency in two specified skills.

Tool Proficiency. Each background gives a character proficiency with one tool—either a specific tool or one chosen from the Artisan’s Tools category. Tools are detailed in chapter 6.

Equipment. Each background offers a choice between a package of equipment and 50 GP.

While the Feats, Skill Proficiencies, Tool Proficiencies and Equipment are all configurable, there is no field to set the three Ability Scores that the Background will allow increases to in a Homebrew Feat.

As per the DMG 2024 DM's Toolbox: 

1: Choose Abilities

Choose three abilities that seem appropriate for the background:

Strength or Dexterity. These abilities are ideal for a background involving physical exertion.

Constitution. This ability is ideal for a background that involves endurance or long hours of activity.

Intelligence or Wisdom. One or both abilities are ideal for a background that focuses on cerebral or spiritual matters.

Charisma. This ability is ideal for a background that involves performance or social interaction.

This step cannot be homebrewed.

Is this intended to be implemented though?