Games like Siege the Day
Games like Siege the Day include Forts, Foxhole, Space Engineers, Mindustry, and Totally Accurate Battle Simulator. We matched them by the tags players give Siege the Day on Steam (Wargame, Base Building, Turn-Based Tactics, Tower Defense, and Strategy): closest matches first, and among equally close ones the better-known games.

Forts
Shared: Base Building · Strategy · Building

Foxhole
Shared: Wargame · Base Building · Sandbox

Space Engineers
Shared: Building · Sandbox · Base Building

Mindustry
Shared: Base Building · Tower Defense · Strategy

Totally Accurate Battle Simulator
Shared: Sandbox · Strategy · PvP

Total War: WARHAMMER II
Shared: Strategy · Turn-Based Strategy · PvP

Squad
Shared: PvP · Wargame · Multiplayer

Thronefall
Shared: Tower Defense · Strategy · Base Building

7 Days to Die
Shared: Base Building · Multiplayer · PvP

Legion TD 2 - Multiplayer Tower Defense
Shared: PvP · Tower Defense · Strategy

Heroes of Might and Magic: Olden Era
Shared: Strategy · Turn-Based Tactics · Multiplayer

Kingdom Two Crowns
Shared: Tower Defense · Base Building · Building

The Riftbreaker
Shared: Base Building · Tower Defense · Multiplayer

Prison Architect
Shared: Base Building · Building · Sandbox

Besiege
Shared: Sandbox · PvP · Building

Factorio
Shared: Base Building · Strategy · Sandbox

WARDOGS
Shared: PvP · Wargame · Multiplayer

Bloons TD 6
Shared: Tower Defense · Strategy · Multiplayer

Garry's Mod
Shared: Sandbox · Building · Multiplayer

Rust
Shared: PvP · Building · Multiplayer

ARK: Survival Ascended
Shared: Base Building · Multiplayer · Building

Creeper World 4
Shared: Wargame · Tower Defense · Building

Mechabellum
Shared: Wargame · PvP · Strategy

Scrap Mechanic
Shared: Building · Sandbox · Base Building