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But, are you contributing to the network?
That is kinda myth. The main goal of running a full node is to validate your OWN txs. After that is keeping decentralized the Bitcoin network. You are not contributing too much if your full node is just sitting there and not seeding also to many other nodes.
can your node be awake 24/7 on a mobile phone without sucking your battery?
Yes. Look into how Neutrino works or lite nodes. A good scenario is:
  • you have a full BTC node at home/office/whatever VPS running 24/7/365 just to provide you blocks through neutrino and electrum server. Nothing else. If you need more apps and solutions, you can run them on a separate machine and just use that node as you need.
  • to that full node you can connect all your LN node mobile devices (clearnet/IP/VPN/tailscale etc) and sync whenever you need the blocks.
A mobile LN node is a "private" node, it doesn't need to be online all the time, just when you need to do a payment and is using only "private"/unannounced channels. Just for your personal use of BTC and LN is enough. You run your node in a private mode.
Read all my guides on https://darthcoin.substack.com and you will find out more.