You've been handed a ~$6,000/mo architecture where nothing is right: a web tier and an API tier both on prev-gen on-demand instances in a single AZ, an oversized Multi-AZ database, and terabytes of cold data in S3 Standard — and there's no CDN or cache at all.
Targets: 8,000 rps, p99 ≤ 130 ms, 99.95% availability, critical durability, under $1,600/mo. Add the edge/cache components the design needs, right-size both compute tiers, fix the storage class, and don't add anything that doesn't earn its cost.