Unable to install self-signed extension when developer mode is off on Linux

[btlechowski]

Follow up to #15024. The test plan (brave/brave-core#8392) for Linux requires to install the extension when developer mode is off. This is not possible.

Note: it is possible to install the extension when developer mode is on

Steps to Reproduce

1. Use steps for Verify you CAN install on Linux from Match Chromium behavior for extension loading brave-core#8392

Actual result:

Unable to install extension
A save prompt is shown after dragging the extension

Expected result:

Able to install extension

Reproduces how often:

Easily reproduced

Brave version (brave://version info)

Brave	1.25.60 Chromium: 90.0.4430.212 (Official Build) beta (64-bit)
Revision	e3cd97fc771b893b7fd1879196d1215b622c2bed-refs/branch-heads/4430@{#1429}
OS	Ubuntu 18.04 LTS

Brave	1.26.22 Chromium: 91.0.4472.57 (Official Build) nightly (64-bit)
Revision	e3443317fa07f1e9997e4a9c738eddfefc3c0292-refs/branch-heads/4472_54@{#6}
OS	Ubuntu 18.04 LTS

cc @brave/legacy_qa @bsclifton