Why won't my Bluetooth headphones connect to two devices at once?
Because that capability is a specific feature called multipoint, and a great many headphones simply do not have it.
What multipoint is. The ability to maintain active connections to two (occasionally three) devices simultaneously, so audio can switch between them without disconnecting and re-pairing. Connect to a laptop and a phone, and a call on the phone interrupts the laptop's audio automatically.
Why it is not universal:
It is optional, not part of core Bluetooth audio. Manufacturers implement it or do not.
It costs resources — maintaining two links uses more power and more processing, and has historically been associated with slightly reduced battery life and occasional instability.
It has sometimes been traded against other features. Some manufacturers have disabled it when using high-bandwidth codecs such as LDAC, because maintaining two connections and a high-bitrate stream together is demanding. You may have to choose.
It was removed and later restored on some product lines, which caused genuine annoyance among users who expected it.
What is often confused with it:
Paired is not connected. Headphones remember many pairings but connect to only one device at a time without multipoint. Reconnecting to a different device means disconnecting from the first, and this is what people experience as the headphones "forgetting".
Fast pair and quick switch features within one ecosystem — Apple devices sharing an iCloud account, for instance — look like multipoint but work differently, and generally only within that ecosystem.
If you have multipoint and it misbehaves: switching is often determined by priority rules that are not obvious, video can lag behind audio when two links are active, and the feature sometimes needs enabling in a companion app rather than being on by default.
If you do not have it: the workaround is disabling Bluetooth on the device you are not using, which forces reconnection to the other.
Check the specification explicitly before buying, since it is rarely prominent.