P1 is not required, Entra ID Free is all that's required to register devices to the directory and use the Azure login on the device. M365 Business Standard has this requirement met, as it has the O365 variant of Entra ID with even more functionality.
P1 is required for Conditional Access policy, which lets you do cool things like require an Entra joined device or an Intune Compliant device.
But no, M365 Business Standard will allow you to join devices to the directory (So will Basic), however the tenant may have been configured to resist this from an end user. Have you tried joining it with a Global Admin account? If you do this, you'll need to use the net use command manually on the endpoint to grant local admin rights. M365 Business Standard lacks the tools you need to automate these processes, but you very much can perform many of them manually.
However yes in general Business Basic and Business standard are a set of collaboration tools only, security functionality comes with PREMIUM, as it contains the Entra ID Premium P1 entitlement, as well as Defender for Business, and Intune. Without these features you're doing a ton of busy work because the client wants to be cheap, this is your idiot tax.
Keynote, joining a machine to Entra ID comes with Entra ID Free, and is therefore included in Entra ID O365 which you have from Business Basic / Standard. The error you started this thread with was a failure to join Intune, Intune enrollment is utterly separate from Entra ID enrollment. This isn't Active Directory, you don't get a free policy engine (Group Policy) with Entra ID. Entra ID is purely an identity provider.