What alternatives can I use to achieve a similar configuration to an L2/L3 VPN without relying on MPLS?
Scenario:
Site1 > ISP1-R1 VRF > ISP1-R2 > ISP1-R3 VRF > Site2
Note: This is for research purposes, not for production.
What is the Legacy and Newer options available?
Literally a bajillion technologies. If you want a real answer you need to give us more information and demonstrate that you did at least a little bit of your own legwork.
VXLAN + BGP evpn? True vrf / multiple forwarding tables without MPLS transport or service labels
You can technically run MPLS over GRE tunnels and then use your familiar L2VPN config, it’s just a lab after all :-).
But really there are so many options that what’s best/easiest is vendor- and implementer-specific. Off the top of my head: GRE, IPsec, wireguard(L3), IP-IP (L3), OpenVPN, different SD-WAN flavors, etc. are all options and I’m sure to be forgetting more. If you have a specific platform or requirements in mind someone may be able to give you a better answer.
Not enough information.
Are you trying to extend VRF’s between sites and use the ISP as transit / underlay?
Look at Extreme Networks or NOKIA or Alcatel’s SPBm solutions. SPBm was made for this.
with that said, of those three, Extreme has the cleanest solution.
NOKIA and AL did their TLV’s for VRFs and Multicast a little differently. the config is not as straightforward as Extreme’s.
Look into SPB (802.1aq)
It’s growing on me quite a lot, and it’s dead easy to configure. And while designed as the evolution of STP, it can do L3 as well as it does L2, and natively.
SD-WAN would be a good choice, but also 802.1aq SPBm.
L3 FEoIP is fantastic; not only are you able to stretch L3VSNs with IP Shortcutting, but also able to stretch L2VSNs over this as well. There is some TE that can be done, if needed, and it is capable of linerate as well.
SPBm is known as MPLS 2, since it’s also similar in operation to layer 2.5. 
It’s super, insanely easy, to setup and configure.
Honestly, probably a SD WAN.
Zerotier + FRR + Linux distro of choice
SRv6 - similar to MPLS but encapsulates the traffic in IP instead of labels.
Cisco SD-WAN - uses MPLS for VPN labels and IPSEC or GRE for transport.
I have never done it, but I would think you could use GRE to tunnel separate LANs back to a central router to a trunk with different vans and then in that router do virtual routing tables without MPLS used.
While L3VPN have traditionally been synonymous with MPLS, in modern SP networks SRv6 END.DT4/END.DT6 might be used to build L3VPN solutions instead. This could in theory work over the internet, but i would wish anyone trying good luck. For your enterprise focused usecase any VPN protocol could work as an L3VPN replacemnt, you could build it youself, or you could go SD-WAN
MPLS is a tunneling technology. There’s lots of similar, IP-based, tunneling technologies that does the same thing. Perhaps not at the same scale as labels are quite hard to outscale, but still.
Yeah… Per-Packet SD-WAN
Any overlay like ipsec/segment routing… can deal with it
GRE is simple enough for L3 tunnels, L2TPv3 if you want L2 tunnels. As other comments have said your requirements are not clear, there are many different options. Understanding what components you have might constrain which options you might have.
VxLAN over IPSec, EoIP over IPSec, OpenVPN “tap” interface, GRE over IPSec, L2TP over IPSec, dozens of other solutions based on actual needs.
is this not literally that basically any S2S VPN can do
More over, is this not what the magical “SD-WAN” buzzword is all about
This is quite literally the best answer OP. Lay out your requirements and challenges(this is an academic/research exercise no?), understand your available options, narrow them down until you’ve landed on the best balance for what you need.