The bug

The player's horizontal movement/momentum doesn't affect the motion of projectiles fired by crossbows at all. Other projectiles (e.g. arrows shot by bows, thrown snowballs, tridents) are not affected by player movement in certain situations:

• Walking/sprinting (e.g. with a high level of the Speed effect)
• Creative mode flying
• Riding an entity (e.g. Minecart, Boat, Horse)

The player's speed is added to the speed of fired projectiles in the following situations:

• Falling
• Flying with Elytra
• Launching oneself with a trident enchanted with Riptide
• Being knocked away by an entity (e.g. the Ender Dragon, or a mob with a Knockback sword)

How to reproduce

• Fly forward, backward or sideways in Creative mode and shoot a projectile (e.g. arrow, non-Riptide trident, ender pearl)
• Alternatively, give yourself a high level of speed (e.g. 30) and throw projectiles while running around

Note that the projectile doesn't take the player's speed into account.

• Enchant a trident with Riptide III (/enchant @s riptide 3)
• Set weather to rain with /weather rain
• Launch yourself with the trident, then shoot a projectile
• Alternatively, fly up 70+ blocks, then start falling and shoot a projectile while falling

The projectile should now be affected by the motion of the player.

Demonstration video