The simple answer is: "As long as it takes for you to reach the singing level and goals you want to achieve with your voice."
It also depends on your current skill level and where your voice is at. It could take 6 months or 6 years, everyone is on a different level and has different goals.
Consistent weekly practice will help you achieve your goals a lot quicker.
If there are any vocal problems that need to be addressed (e.g. like singing out of tune) this should be considered as it can take longer to see vocal improvement when there are issues that need to be worked through.
Unlearning bad habits (like pushing/shouting) is probably what takes the most time to resolve. Unfortunately there are no "quick fixes" or "magic tricks" when it comes to proper technique, it does take time to develop good vocal technique, especially if you want to prevent any future problems and health issues with your voice. A good basic foundation, correct singing technique and knowing how your voice works is key to vocal longevity.
You need time to learn muscle memory, build stamina, strength, flexibility, good posture, breathing, articulation, resonation, placement, to name a few.
The thing with singing, is the more you learn, the more you realise there is to learn. The voice really is a complicated, multi-faceted and wonderful instrument.
Once you've reached the vocal level you want to achieve, you should then upkeep this with regular exercises.
The voice is a combination instrument that works best when all its components are working together in harmony and a lot of problems arise when this is not happening.
Each voice is unique and has its own unique qualities. You will find yours when you spend time experimenting and finding out how your voice works.
Discovering your own voice is very rewarding and when you have learnt to balance your voice and master your instrument, you will absolutely love "playing" it.
People may sometimes be put off singing and think that they can't sing or that they just don't have any natural talent because of problems like: their voice doesn't sound good to them, they sing out of tune, their voice cracks or breaks, they may have problems hitting any high notes, have no vocal power, run out of air, strain, etc.
This is really not true, anyone with a healthy voice can learn to sing and overcome vocal problems. Your voice is made up of a lot of different components that need to be balanced and used together and imbalances result in vocal problems, as mentioned above. Just like a cake is made up of ingredients (some not nice on their own), combined they are delicious. It really is about knowledge and learning about your entire voice and how to use it.
Singing should never hurt or feel unpleasant, even when you are singing at your loudest. There are specific techniques involved in "high pressure singing" and it isn't shouting.
Learning about the voice and how to use it correctly with healthy technique will ensure you can use your voice for a lifetime.
You are your voice. Investing in your voice, is investing in yourself. You are worth that investment.