Ah ok. So to answer your question, you would need to put it into a specific tag and then overwrite the vanilla recipe. By default, Forge replaces almost all instances of iron ingot with 'forge:ingots/iron' through their recipe provider. The few that remain are iron block and iron nugget (since they are specific to the block version). So, as long as both items are in the specific tag and the tag is referenced in the recipe, it will take in anything within that tag (which would be your modded item). Do remember though if you plan on using something similar to ForgeRecipeProvider's implementation to replace the item with a tag that you exclude items that would be exclusive to that item set. Else, there will be even more issues with commonalities between recipes.
Since the items are more abstract, you might not want to use a forge domain for your tags. One of the examples I can point you towards is endermen holdable blocks. This is a tag used to determine if an enderman can hold a certain block. This has a lot of different items that are not related to each other. However, they are for a unique purpose. In your case, if the items you want inputted cannot be condensed to a common group, then it would be best to just use a unique tag specific to your mod rather than a forge tag. And I assume when you say 'mark their tags manually,' you mean create the variable that holds your tag instance. If you would like to use it in your code then yes. If it's only for reference in recipes or advancements, you don't specifically need to. I do it because I use data generators to create tags for me. And you can add to already existing tags without replacing the data within them as long as "replace" remains false in the json file. Hopefully I have answered your question.