Part of the work of terraform init is to install all of the required providers into a temporary directory .terraform/providers so that other Terraform commands can run them. For entirely new providers, it will also update the dependency lock file to record which versions it selected so that future terraform init can guarantee to make the same decisions.
If you are running terraform apply tfplan in a different directory than where you ran terraform plan -out=tfplan then that local cache of the needed provider plugins won't be available and thus the apply will fail.
Separately from that, it also seems that when you ran terraform init prior to creating the plan, Terraform had to install some new providers that were not previously recorded in the dependency lock file, and so it updated the dependency lock file. However, when you ran terraform apply tfplan later those changes to the lock file were not visible and so Terraform reported that the current locks are inconsistent with what the plan was created from.
The Running Terraform in Automation guide has a section Plan and Apply on Different Machines which discusses some of the special concerns that come into play when you're trying to apply somewhere other than where you created the plan. However, I'll try to summarize the parts which seem most relevant to your situation, based on this error message.
Firstly, an up-to-date dependency lock file should be recorded in your version control system so that your automation is only reinstalling previously-selected providers and never making entirely new provider selections. That will then ensure that all of your runs use the same provider versions, and upgrades will always happen under your control.
You can make your automation detect this situation by adding the -lockfile=readonly option to terraform init, which makes that command fail if it would need to change the dependency lock file in order to perform its work:
terraform init -lockfile=readonly
If you see that fail in your automation, then the appropriate fix would be to run terraform init without -lockfile=readonly inside your development environment, and then check the updated lock file into your version control system.
If you cannot initialize the remote backend in your development environment, you can skip that step but still install the needed providers by adding -backend=false, like this:
terraform init -backend=false
Getting the same providers reinstalled again prior to the apply step is the other part of the problem here.
The guide I linked above suggests to achieve this by archiving up the entire working directory after planning as an artifact and then re-extracting it at the same path in the apply step. That is the most thorough solution, and in particular is what Terraform Cloud does in order to ensure that any other files created on disk during planning (such as using the archive_file data source from the hashicorp/archive provider) will survive into the apply phase.
However, if you know that your configuration itself doesn't modify the filesystem during planning (which is a best practice, where possible) then it can also be valid to just re-run terraform init -lockfile=readonly before running terraform apply tfplan, which will therefore reinstall the previously-selected providers, along with all of the other working directory initialization work that terraform init usually does.
As a final note, tangential to the rest of this, it seems like Terraform was also printing a warning about a deprecated language feature and on your system the warning output became interleaved with the error output, making the first message confusing because it includes a paragraph from the warning inside of it.
I believe the intended error message text, without the errant extra content from the warning, is as follows:
Error: Inconsistent dependency lock file
│
│ The following dependency selections recorded in the lock file are
│ inconsistent with the configuration in the saved plan:
│ - provider registry.terraform.io/hashicorp/aws: required by this configuration but no version is selected
│ - provider registry.terraform.io/hashicorp/external: required by this configuration but no version is selected
│ - provider registry.terraform.io/hashicorp/google-beta: required by this configuration but no version is selected
│ - provider registry.terraform.io/hashicorp/google: required by this configuration but no version is selected
│ - provider registry.terraform.io/hashicorp/local: required by this configuration but no version is selected
│ - provider registry.terraform.io/hashicorp/null: required by this configuration but no version is selected
│ - provider registry.terraform.io/hashicorp/random: required by this configuration but no version is selected
│
│ A saved plan can be applied only to the same configuration it was created
│ from. Create a new plan from the updated configuration.
╵
