You have to understand a very simple thing: LEDs are current limited, not voltage limited.
This means the amount of current that goes through the LED must be limited, otherwise the LED will be damaged, will blow up.
So once the voltage is above the forward voltage of a LED (a value which varies depending on the chemicals used to make the LED, and it's between around 1.7v for red leds, 2..2.2v for amber / green leds and 2.8v..3v for blue/white leds) the led turns on and lets any amount of energy flow through it. If you let too much energy go through it, the led overheats and gets damaged.
You can limit the amount of current going through the led with various methods, but the most simple one is to put a resistor in series with the led.
So for example, if you have a single white led with 3v forward voltage which can consume up to 20mA safely and you want to power it with 5v from a usb charger (power bank, phone charger, doesn't matter), you want to pick a resistor in such a way that the led will only "see" 20mA go through it. So you use the formula:
Input voltage - Forward voltage of led = Current x Resistance value.
so if we put the values in our example in the formula: 5v - 3v = 0.02A (20mA) x R ===> R = 2v / 0.02 = 100 ohm
Now in your string of leds powered by 2 AA batteries.
You have to understand that there's a difference between a battery powered circuit and a circuit powered by a power adapter (doesn't matter if it's AC or DC).
A battery has an internal resistance, it can only push so much current before the battery itself overheats and the voltage drops. So you have to imagine the battery as a power adapter PLUS a resistor in series with the power adapter.
In the case of AA batteries, these typically can output up to around 1-2A (2000mA) of current ... so you can look at that chain of leds and count how many leds are there.... i count about 20 leds.
So if you had ideal batteries that can output continuously 2000mA of current, these 2000mA of current would be evenly split across the 20 leds, so each led would get 100mA.
So you already have an inherent current limitation without adding a resistor to each led, to make sure it doesn't blow up.
You also have to keep in mind that the wires are not ideal, they have some resistance... so you see that chain of leds has 20 leds and it's maybe let's say 2 meters long... that means that between the + and - poles of the battery there's going to be 4 meters of wire.
The resistance of the wire will vary depending on the thickness of the wires... let's say that those wires are AWG24 ... if you look at an AWG table, you can determine that's a resistance of around 85 mOhm per meter of wire :
https://en.wikipedia.org/wiki/American_wire_gauge#Tables_of_AWG_wire_sizes so with 4 meters of wire, you have around 0.4 ohm of resistance in the wires alone. Keep in mind that the resistance value is for copper, while these cheap led strips may use a mix of copper and steel wire, or steel and aluminum wires, because steel and aluminum is cheaper... so let's go with 0.5 ohm of resistance in the wires alone.
So the battery behaves like there's a resistance inside it, and the wires also have some resistance, and all this resistance prevents the battery from pushing too much current in the chain of leds, so those 10-20 leds will receive maybe a bit more current than what it's recommended when the batteries are fully charged, but the leds will survive because the wires will behave like a heatsink, sucking the heat from the leds and dissipating it over the long wires.
This design works for cheap stuff like those 10-20 leds powered by 2 batteries sold for 1-2$, because nobody will request refunds or complain if they die 1-2 months after Christmas.
If some led dies, the other will continue to work because they're all in parallel, but keep in mind that the rest of the leds now receive more current, so they're more "stressed" and the risk of another one failing increases. If too many die, the other will also die, because there's no resistor for each individual led, to protect it.
However, if you use a power adapter, this power adapter will have much lower internal resistance, instead of let's say 50 ohms of internal resistance, the power adapter will have maybe 5-10 ohm of internal resistance, so this resistance along with the resistance of the wire will not be big enough to limit the current going to the leds and the leds will blow up.
In chains of leds designed to be powered with an adapter, you will often see a tiny resistor at the base of each led, or in the socket where the led is placed.
Or, you may see a resistor hidden inside the wire going to groups of 3 leds, for chains of leds designed to be powered by 12v (3 x 3...3.2v = ~ 10v, 12v is used to account for losses in the long wire all the way to the last led)
So how can you convert that 10-20 led chain of leds (in parallel) powered by 2 batteries to work with DC adapter.
Well, you have to add the resistance that's hidden in the battery.
Pick the amount of current you want for each led and determine what voltage you're gonna use to power that chain of leds where the leds are all in parallel.
Let's go with 5v and 10mA for each led that's white and has a forward voltage of around 3v ... so if you have 20 leds on the chain, you would have 20x 10ma = 200mA or 0.2A
So going back to that formula : 5v - 3v = 0.2 A x R so R = 2 / 0.2 = 10 ohm
So if you add a 10 ohm resistor to this chain of leds, you can power them from a 5v adapter, and they should not consume more than 200mA. In reality they'll consume a bit less, because those meters of wire also have a tiny resistance (less than 1 ohm)
If you want to power 3 such chains from the 5v adapter, you can put one 10 ohm resistor at the start of each chain, and connect them in parallel to your adapter. Each chain will only consume up to your calculated current value (the 200mA in my example).
If you want to be more efficient you can re-arrange the leds to have groups of leds in series, then these groups you can place in parallel .
For example, let's say you have a 12v power adapter, or you want to power some leds from a computer power supply.
You know that the forward voltage of a single white led is around 3v, so you can realistically only put 3 leds in series (3 x 3v = 9v) because 4 leds will be exactly 12v, and your power supply may not always be exactly 12v.
So you can make a group of 3 leds and put a resistor in series with this group of 3 leds and that resistor will protect the group of 3 leds:
12v (input voltage) - 3 leds x 3v (forward voltage of led) = 0.01A (10mA current for the group of leds) x R => R = 3v / 0.01 = 300 ohm, so I'd use one of the standard values like 270 ohm (which would give a tiny bit more current through the group) or 330 ohm (a bit less current)
Now, you can take these bits of 3 leds + resistor and connect them in parallel , as many as you want, and the total power consumed will be number of groups x ~ 10mA (current for each group of leds plus resistor)