Can you combine a Battle Master Maneuver like Trip Attack and its 1d8 damage with True Strike, Booming Blade, Green Flame Blade, etc., since you're making an attack roll and using a weapon in the spell's casting?

TIA

Yes you can use Trip Attack when you hit a creature with a weapon attack, including via spells.

I'd say it's also fine for these Maneuvers:

• Disarming Attack: "When you hit a creature with an attack roll..."
• Distracting Strike: "When you hit a creature with an attack roll..."
• Goading Attack: "When you hit a creature with an attack roll..."
• Maneuvering Attack: "When you hit a creature with an attack roll..."
• Menacing Attack: "When you hit a creature with an attack roll..."
• Precision Attack: "When you miss with an attack roll..."
• Pushing Attack: "When you hit a creature with an attack roll using a weapon or an Unarmed Strike..."

And if you're using a melee weapon, then:

• Sweeping Attack: "When you hit a creature with a melee attack roll using a weapon or an Unarmed Strike..."

Also wanted to add that RAW you could use the maneuvers that don't specify a weapon or unarmed strike on other cantrips or spells besides just the weapon ones. The maneuvers specify when you can use them and other than sweeping and pushing they only say when you hit or miss a creature with an attack roll. There's probably some weird combos using precision attack to make spells like Bigby's hand hit.

Assuming 2024 yes, because 2014 Maneuvers only Grappling Strike could work on a melee spell attack, others that hit require a weapon.