logtail: prevent js/wasm clients from picking TLS client cert

Corp details:
https://github.com/tailscale/corp/issues/18177#issuecomment-2026598715
https://github.com/tailscale/corp/pull/18775#issuecomment-2027505036

Updates tailscale/corp#18177

Change-Id: I7c03a4884540b8519e0996088d085af77991f477
Signed-off-by: Brad Fitzpatrick <bradfitz@tailscale.com>
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