It is not hard, you are just required to be more knowledgeable.
Perhaps … I haven’t checked Linux Mint for years …
But it is solved - you got the instructions - you just don’t apply the instructions correct.
Surely you need to use the filenames relevant to your usecase. The wiki is generic - the filenames change on every release.
As you already verified the checksum - and it passed - the ISO is complete - really no need to also verify the signature although the signature will confirm the ISO originates from the Manjaro Team or team members.
Since you already fetched both ISO and signature - open a terminal and navigate to the folder where you keep the downloaded files, and jump to step 3
Handholding part
explanantion
The two files in the same folder - don’t import any keys - simply verify the signature against the file
gpg --verify <filename.sig>
If you want to start over then you can use wget to fetch the full ISO and the signature - then verify the download using the signature.
The output illustrates the result of running the commands on my system 2023-08-21T22:00:00Z to download and verify the current cinnamon ISO
step 1 - fetch ISO
wget https://download.manjaro.org/cinnamon/22.0/manjaro-cinnamon-22.0-230104-linux61.iso
07:43:47 ○ [fh@tiger] ~/temp
$ wget https://download.manjaro.org/cinnamon/22.0/manjaro-cinnamon-22.0-230104-linux61.iso
--2023-08-22 07:43:58-- https://download.manjaro.org/cinnamon/22.0/manjaro-cinnamon-22.0-230104-linux61.iso
Loaded CA certificate '/etc/ssl/certs/ca-certificates.crt'
Resolving download.manjaro.org (download.manjaro.org)... 195.181.170.19, 156.146.33.141, 195.181.175.41, ...
Connecting to download.manjaro.org (download.manjaro.org)|195.181.170.19|:443... connected.
HTTP request sent, awaiting response... 200 OK
Length: 3837229056 (3,6G) [application/octet-stream]
Saving to: ‘manjaro-cinnamon-22.0-230104-linux61.iso’
manjaro-cinnamon-22.0-23010 100%[=========================================>] 3,57G 13,2MB/s in 4m 35s
2023-08-22 07:48:33 (13,3 MB/s) - ‘manjaro-cinnamon-22.0-230104-linux61.iso’ saved [3837229056/3837229056]
step 2 fetch signature
wget https://download.manjaro.org/cinnamon/22.0/manjaro-cinnamon-22.0-230104-linux61.iso.sig
07:48:33 ○ [fh@tiger] ~/temp
$ wget https://download.manjaro.org/cinnamon/22.0/manjaro-cinnamon-22.0-230104-linux61.iso.sig
--2023-08-22 07:48:45-- https://download.manjaro.org/cinnamon/22.0/manjaro-cinnamon-22.0-230104-linux61.iso.sig
Loaded CA certificate '/etc/ssl/certs/ca-certificates.crt'
Resolving download.manjaro.org (download.manjaro.org)... 156.146.33.137, 156.146.33.140, 195.181.175.15, ...
Connecting to download.manjaro.org (download.manjaro.org)|156.146.33.137|:443... connected.
HTTP request sent, awaiting response... 200 OK
Length: 438 [application/octet-stream]
Saving to: ‘manjaro-cinnamon-22.0-230104-linux61.iso.sig’
manjaro-cinnamon-22.0-23010 100%[=========================================>] 438 --.-KB/s in 0s
2023-08-22 07:48:46 (15,8 MB/s) - ‘manjaro-cinnamon-22.0-230104-linux61.iso.sig’ saved [438/438]
step 3 verify signatrue
gpg --verify manjaro-cinnamon-22.0-230104-linux61.iso.sig
07:48:46 ○ [fh@tiger] ~/temp
$ gpg --verify manjaro-cinnamon-22.0-230104-linux61.iso.sig
gpg: assuming signed data in 'manjaro-cinnamon-22.0-230104-linux61.iso'
gpg: Signature made ons 04 jan 2023 12:37:36 CET
gpg: using RSA key 3B794DE6D4320FCE594F4171279E7CF5D8D56EC8
gpg: Good signature from "Manjaro Build Server <build@manjaro.org>" [unknown]
gpg: WARNING: This key is not certified with a trusted signature!
gpg: There is no indication that the signature belongs to the owner.
Primary key fingerprint: 3B79 4DE6 D432 0FCE 594F 4171 279E 7CF5 D8D5 6EC8
The key point to note is the line indicating good or bad
gpg: Good signature from "Manjaro Build Server <build@manjaro.org>" [unknown]
What to look for
To illustrate what happens if the signature does not match I took the minimal iso and renamed it to match the signature file
08:26:41 ○ [fh@tiger] ~/temp
$ ls -l
total 9180312
-rw-r--r-- 1 fh fh 2781693952 4 jan 2023 manjaro-cinnamon-22.0-230104-linux61.iso
-rw-r--r-- 1 fh fh 3837229056 4 jan 2023 manjaro-cinnamon-22.0-230104-linux61.iso.bak
-rw-r--r-- 1 fh fh 438 4 jan 2023 manjaro-cinnamon-22.0-230104-linux61.iso.sig
-rw-r--r-- 1 fh fh 2781693952 4 jan 2023 manjaro-cinnamon-22.0-minimal-230104-linux61.iso
Then run the verify command once more
gpg --verify manjaro-cinnamon-22.0-230104-linux61.iso.sig
08:26:31 ○ [fh@tiger] ~/temp
$ gpg --verify manjaro-cinnamon-22.0-230104-linux61.iso.sig
gpg: assuming signed data in 'manjaro-cinnamon-22.0-230104-linux61.iso'
gpg: Signature made ons 04 jan 2023 12:37:36 CET
gpg: using RSA key 3B794DE6D4320FCE594F4171279E7CF5D8D56EC8
gpg: BAD signature from "Manjaro Build Server <build@manjaro.org>" [unknown]
It is quite obvious the file does not match the signature.
Result to look for
gpg: Good signature from "Manjaro Build Server <build@manjaro.org>" [unknown]
gpg: BAD signature from "Manjaro Build Server <build@manjaro.org>" [unknown]