check out the Surf Simply 'tree of knowledge' for the way they see progression (you seem like you are toward the top of level 2 - so you can start there and look at the lower end of level 3)
https://surfsimply.com/surf-coaching/th ... knowledge/if you are currently riding down the line, my suggestions are
1. on the right wave, try to go straight down and then do a bottom turn (rather than an angled takeoff) to go along the face. Much easier frontside for most people. Once you have this, now and then see if you can do a really hard bottom turn so that you turn from the bottom straight up the face (you will probably go right over the back of the wave, but thats ok - you are practising the turn not the surfing along the face)
2. at the end of the wave, do a sharp turn either straight toward the beach or up and over the back of the wave (surf simply call this 'trimming to the flats' and then the progression of 'carving to the beach' - note the difference between trimming and carving. There is a surf simply video on this if you google it up)
3. try doing some 'S' curves along the face ie go down at 30/45 degrees then up the face again. Link as many of these as you can (so you are doing a sideways 'S' along the face). It can be hard on short rides, definitely. As you progress, make the turns sharper (eg at first its a pretty flat wavy line, then the curves get sharper and sharper)
4. if you feel like it, try some late drops/takeoffs. Move 7-10ft further in than you are used to and see if you can catch the waves
You can see that most of these suggestions (and just my opinion, no science there) are to start doing turns. Make sure you do the turns properly eg hand positioning, head position, leg compression and extension, foot over the fins and weighting over the fins). You can 'muscle' a board through small turns without much technique, but as soon as you start trying sharper turns that stops working.
oh, and dont do all of these on the same wave - just pick one or two options and do them, on different waves, during a surf session. Maybe spend 8 waves doing turns and the rest of your time just having fun and doing whatever. If you fall over in your first 8 waves because you are trying things, thats ok, because you will have the rest of your session to surf along the face (surf coaches commonly say that the biggest hurdle to beginner surfing development is that surfers want to maximise the time surfing ie standing up; and thus minimise any risks that might cause them to fall ie trying new things. So the solution is to spend part of your time trying new things and part of your time going back to the natural behaviour of maximising time on the face)
There are plenty of web resources to assist with turning technique. One of our frequent posters/master surfers (waikikichan) has a blog with a lot of technical tips for turns (scroll through the many entries!)
http://alohaki.jugem.jp/ Of course, above all, just keep enjoying yourself. If you are having fun and in 10 years time all you can do is an angled take off and surf along the face and you are still having fun, then you are a success.
[edit: the other thing you could look at doing is creating speed, which can mesh in with some of the above
https://surfing-waves.com/surfing-speed.htm )