Can I play Minecraft Java if I only buy the Windows 10 version

I do not own Minecraft outside my PS4, I know I can't play either Windows 10 or Java with that purchase. However, my primary computer is Linux and only supports the Java edition, and its past the deadline to get a redeem code for Windows 10 edition if I purchase the Java Edition.

Can I purchase the Windows 10 edition and use that purchase to login and play on the Java edition?

No, You are unable to buy Windows 10 (Bedrock Edition) and get Java Edition for free.

However, if you bought Java Edition before October 19th 2018, you are able to redeem a free copy of Bedrock Edition on https://mojang.com/.

Following link details further. https://help.mojang.com/customer/en/portal/articles/2064007-minecraft-for-windows-10

The links provided in this previous answer are now broken. Mojang have updated their website to redirect to Minecraft.net - but you can still access your Mojang account using the link at: http://account.mojang.com/login

Here's a guide from Mojang support: https://help.minecraft.net/hc/en-us/articles/360035130391-Minecraft-for-Windows-10

Players who have purchased Minecraft: Java Edition before October 19th, 2018 can get Minecraft for Windows 10 for free by visiting their Mojang account. Log into account.mojang.com, and under the “My Games” heading you will find a button to claim your gift code. If you purchased Minecraft: Java Edition after October 19th, 2018, the button will not be there, so if you’re unsure of when you purchased Minecraft: Java Edition, that’s a good way to check. Pressing the button will generate a token and send you to a Microsoft redemption page.

If you have an older Minecraft account (you still log in with your username), visit this article to find out about account migration. Once you’ve migrated your account, you will be able to claim a code for Minecraft for Windows 10.

You must be signed into a Microsoft/Xbox Live account in order to redeem the code. Please note that you cannot move the license once the code has been redeemed. Your code is saved on your Mojang account page for future reference.