my current version is 2023 10 02 , will it be okay to download the lastest version patch ?

The "update files" contain only the files that have been changed since the last update. If you skipped an update, you can't use them, or you'll miss the files that have been changed in between.
The "update files" always tell you in the file name for what version they can be used. The last files are "Renryuu Ascension 23.11.23 - Update files for version 23.11.16 or later only!"
The version number is in "year - month - day" format, which means your version is from October, while the update files are for the version of the 16th November.
It's possible to use the MEGA folder with old update files, to install them one by one in the right order, but it's usually better and safer to download the full version instead. When you download the full version again, you can copy&paste the content of the www/save folder (ALL of it!) of the old game folder to the same folder in the new game version.

Old update files: https://mega.nz/folder/C8RnkahS#VJqSqj4Vi0WOsxKj_SmyEw