Taking the Shrine

The shrine is guarded by 20 kobolds, 10 winged kobolds, 3 cult fanatics, and 1 dragonshield (from Volo's). The layout of the shrine is included with the positions of the kobolds marked on it.
The three guards on the hillside are marked, with 2 kobolds to the left of the opening, and 1 winged kobold concealed to the right of the cave entrance.
The scale for this sketch is mostly to show relative position. Feel free to stretch or adjust for the game you're running.
This encounter scales out at roughly 3rd level, but a weaker party should be fine going through it as a series of smaller encounters. For this, just assume the connecting corridors are longer. For a higher level starting party, have the encounter draw the attention of the rest of the shrine. Fighting everything at once is closer to 5th level as an encounter.
Ideally, the party is able to maintain some stealth in dealing with the guards outside. If so, allow them to move through the shrine from room to room making stealth rolls against the perception of the kobolds. I didn't mark the prisoners on the map, but I picture 5 survivors of the attack on the outpost being held in the half-excavated room behind the actual shrine room (1F, 2W, 1K). Once the party reaches the stairs, stealth is really no longer an option, but if they are quiet and patient and cunning, they could potentially slip around the corner near the stairs and eliminate all of the cultists in the warren of chambers before going up the stairs to the main shrine.
I think a nice twist to ramp up the encounter at the shrine would be if the necklace awoke the statues once it is within the chamber. That could be a side effect of the artifact, that it animates statues. Whether they attack or can be controlled by the user is an interesting question, and could depend on the battle and what works best to balance it. I think a better option would be to have the player with the necklace make an arcana check DC15 to control the statues, otherwise they are hostile and attack. Learning more about the artifact, or just spending more time attuning to it, could improve the threshold for success or eliminate the need for a roll, at the discretion of the DM.
The tunnels lead beyond the shrine into the mountain, leading to further investigation and exploration, if desired. The ones beyond the shrine and unfinished room look newly excavated. They are the tunnel that the kobolds rediscovered the shrine from. It looks as though they accidentally broke through into a secret room behind the shrine, and have been expanding the opening and room as an access point to the shrine.