As someone who is familiar with this module and has DM'ed a few sessions of 5e, I can definitely say it's faithful to the module its based on and the mechanics of D&D 5e... perhaps a bit too faithful because combat is a festive of party members and monsters evading each other left and right as if they were completely missing their target roll number. Definitely reminded me of the first few sessions my group went through as level ones, haha.
The maps and placement of enemies are spot-on, as well as the spells and cantrips for the party members. The variety is nice, but it's hard to tell the difference how one spell functions over another. Maybe additional info after the spell's flavor text to explain how the spell targets enemies would help address this. For example, Tasha's Caustic Brew targets all enemies, but that information is only available when you examine the spell out of battle. The Paladin and Sorcerer are also extremely slow. Because of this, it feels a bit unrewarding to wait for their turn because they will almost always miss their attack (except for Magic Missile. I can always count of Magic Missile!)
As I mentioned earlier, because most actions practically miss in combat, I've conditioned myself to only use spells and cantrips. I never depended on a party member's regular attack because they miss too often. I know missing attacks are extremely common in early levels of 5e, but it can be a rather frustrating experience as a player because there isn't a way to increase the odds of our attacks landing. In tabletop 5e, players can manipulate situations and support allies to allow them to roll Advantages, but in a computer-based RPG, there's no way to emulate that.
These were just a few of my thoughts as I killed Klarg and soft-locked myself after killing a large group of Kobolds. My first game was based on an adventure module too, albeit not as faithful as yours. I'm looking forward to see what's next!