That's your red flag right there. All identities that are tied to individual people should be connected to SSO in some way, then there will be no juggling of passwords at all on the individual-person level. Then you only need some 2FA solution on top in your identity provider, for instance TOTP or FIDO, and you're all set. (Corollary: If at all possible, only pick external services that can plug into your company's own SSO.)
For credentials not tied to individual people, e.g. root passwords on devices, my org uses HashiCorp Vault, and we're mostly satisfied with it. It's a bit of a struggle to configure the policies so that each group of (human/technical) users only has access to the secrets that they actually need, but I won't put the blame for that on Vault.