Per board search the Lolin32 is supported – however I don’t see it having an OLED display in the seller pages. The ESP32 boards are quite generic, the 2 basic ESP32 modules are the WROOM and WROVER variants, wheras the latter just has 8MB PSRAM in the module. I’d say pretty much all ESP32 boards work with the Espressif ESP32 Dev Module board config. The difference when choosing a different board that a different board variant of the Arduino core is used, which as assigns some different default pins.
You can pick that framework you like, but the firmwarecode you write then must be targetting that framework. If you’re working with the Arduino IDE, you’re automatically working with Arduino as the framework, so if you want to write code for that, you need to again chose Arduino in PlatformIO. Here’s a topic discussing some basics about frameworks: Frameworks, platforms, and boards, oh my!
See linked topic. By “Platform”, PlatformIO means the general type of microcontroller (series). The ESP32 chips / modules belong to the Espressif32 platform. A board definition only ever belongs to one platform – the Arduino Uno belongs in the “Atmel AVR” platform (since it features an Atmel ATMega328P chip from the AVR series), and to none else.