The steps to upgrade Site Recovery Manager (SRM ) from 8.3 to 8.7 is to follow the release notes in 8.4 (legacy). If current version is SRM 8.3 migrate from Windows to an Appliance 8.4 prior upgrading to 8.6 then to 8.7. SRM versions 8.7.x virtual appliance and 8.6.x virtual appliance upgrade to Site Recovery Manager 9.0.
You can migrate your Site Recovery Manager 8.3.x instance from Windows to the Site Recovery Manager 8.4 Virtual Appliance. For information about the migration procedure, see Migrate from Site Recovery Manager for Windows to Site Recovery Manager Virtual Appliance.
SRM upgrade path https://docs.vmware.com/en/Site-Recovery-Manager/8.4/rn/srm-releasenotes-8-4.html#compatibility
Before upgrading know the upgrade path for Site Recovery Manager by checking the Interoperability.
VMware Product Interoperability Matrixes
For the unpublished information of SRM 8.6 to 9.0. Please also track other VMware products you might have installed that will be impacted by a SRM upgrade and plan accordingly
Compatibility Matrices for VMware Site Recovery Manager 8.6
Compatibility Matrices for VMware Site Recovery Manager 8.7
Compatibility Matrices for VMware Site Recovery Manager 8.8
Compatibility Matrices for VMware Site Recovery Manager 9.0
Compatibility of vCenter version with SRM
Order of upgrading Site Recovery Manager Products with vCenter versions, ESXi versions and VMware Tools