The problem is that when you call from PowerShell (unlike from cmd.exe), the command name dotenv resolves to a PowerShell script, namely dotenv.ps1, as you report.
When PowerShell calls a PowerShell-native command - including .ps1 files - its own parameter binder interprets the (first) -- argument and removes it; that is, the target command never sees it.
(The semantics of -- is analogous to that of Unix utilities: -- tells the parameter binder to treat subsequent arguments as positional ones, even if they look like parameter (option) names, such as -foo.)
Thus, unfortunately, you need to specify -- twice in order to pass a single -- instance through to the .ps1 script itself:
# The first '--' is removed by PowerShell's parameter binder.
# The second one is then received as an actual, positional argument by
# dotenv.ps1
dotenv -e .\.env -- -- pnpm dev --filter api
Alternatively, assuming that dotenv.cmd, i.e. a batch file version of the CLI exists too (and is also in a directory listed in $env:PATH), you can bypass this problem by calling it explicitly, instead of the .ps1; when calling external programs (including scripts interpreted by other shells / scripting engines, such as cmd.exe), PowerShell does not remove --:
# Calling the batch-file form of the command doesn't require
# passing '--' twice.
dotenv.cmd -e .\.env -- pnpm dev --filter api
Caveat: While it will typically not matter, the way a batch file parses its arguments differs from how PowerShell does it for its native commands.
