Pokémon Red and Blue / GAME HISTORY
Why Can One Stat Change Boost Other Stats in Pokémon Red and Blue?
A stat-changing move can reapply bonuses to stats it did not target.
Short answer
Bulbapedia’s battle documentation describes badge bonuses being applied again when a player’s Pokémon has a stat stage changed. The stat being changed is recalculated; other eligible stats can receive another badge boost. It is not a bonus to every stat from every move.
Scope: Original Game Boy Red and Blue; community-documented behavior.

One change can affect more than one number
A successful Double Team or an opposing Screech changes a stat stage. In the documented Game Boy behavior, changing a player’s Pokémon also applies the relevant badge bonuses again. You need the corresponding badges; the effect is not supplied by Double Team alone.
The important distinction is between the stat the move changes and the other stats. The first is recalculated from its out-of-battle value and current stage. Other badge-boosted stats can receive another multiplication by 1.125, even though their badge bonuses were already present.
Why repeated setup changes the comparison
Repeated changes can stack those extra boosts, up to the documented stat cap of 999. Comparing only the named effect of a setup move therefore misses part of what happens in this version. It does not mean the move raises every stat stage.
The later battle rules are separate
The same community documentation records the stat-modification errors as fixed in the Stadium series. That is a difference between battle programs, not an update applied to a Red or Blue cartridge. Modern setup rules should not be read back into an original Game Boy battle.
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