> Our scripts have so many retry loops and arbitrary pauses mixed in
This is unfortunately your fault, not Azure's. Their API is explicitly designed around this eventual consistency and weak references, so your client side must take this into account. Typical bash, Python, or PowerShell scripts are the Wrong approach with a capital W, and you will forever be tearing your hair out if you persist on using them. (Or any similar imperative deployment mechanism)
The only robust method is ARM Templates, or better yet, Bicep templates[1]. The latter simply compile down to ARM, so they're essentially equivalent but terser and with nicer tab-complete.
Compared to scripts, templates have key advantages:
1. Built-in incremental / differential deploy capability. A partially deployed template can be simply redeployed[2] to "fix it up", without requiring client-side logic for every corner case.
2. Can deploy multiple changes that would fail if deployed step-by-step. For example, App Gateway can have intermediate configurations that won't validate on the way to a valid final configuration. This is madness to unravel with scripts. Templates generally just take you to the final configuration in one step.
3. Inherently parallel. Anything that can be deployed concurrently will be. Anything. No need to write complex and error-prone parallel loops on the client side!
4. Largely immune to temporary failures like missing reads after writes.[3] The template engine has a built-in retry loop for most (all?) fallible steps. You'll see it has "failed"... and then "succeeded" anyway.
[1] https://docs.microsoft.com/en-us/azure/azure-resource-manage...
[2] Most of the time. All resources should be idempotent to redeployment, but many aren't because this is not mechanically enforced. IMHO, this is just shoddy, shoddy engineering and everyone involved should be ashamed. Being nearly idempotent is like being nearly pregnant.
[3] You still need a few tricks up your sleeve for robust deployments. Anything outside of ARM, such as Azure AD groups and RBAC tend to be a PITA. Generally you want to wrap your deployments in a script that takes the object GUID of the created group and feed that into the template. That works, because the GUID can be used even if the full object is not fully replicated around yet.