In the current micropython git master we get following memory in an ordinary ESP32 without SPI RAM right after boot:

>>> esp32.idf_heap_info(esp32.HEAP_DATA)
[(7288, 176, 0, 176), (16648, 5608, 4096, 40), (94064, 5684, 4096, 5664), (15072, 13448, 8192, 13448), (113840, 112216, 65536, 112216)]
>>> micropython.mem_info()
stack: 704 out of 15360
GC: total: 64000, used: 1504, free: 62496
 No. of 1-blocks: 20, 2-blocks: 15, max blk sz: 18, max free sz: 3894

so we have 62496 bytes available for python, 137132 for C malloc()

The changed memory layout of ESP32-S2 changes the ratio strongly in favour of micropython heap:

>>> esp32.idf_heap_info(esp32.HEAP_DATA)
[(8148, 140, 0, 140), (197736, 38728, 32768, 34264), (14864, 13108, 8192, 13108)]
>>> micropython.mem_info()
stack: 704 out of 15360
GC: total: 128000, used: 2640, free: 125360
 No. of 1-blocks: 39, 2-blocks: 18, max blk sz: 32, max free sz: 7829

So on S2 we have 125360 bytes available for python and only 51976 bytes in IDF heaps for C malloc()
This gets exhausted just by connecting WiFi (STA mode with WPA2 PSK) and WebREPL request from network.

IMO we need to adjust mp_task_heap_size at ports/esp32/main.c:124

size_t mp_task_heap_size = heap_caps_get_largest_free_block(MALLOC_CAP_8BIT);

to better reflect the lower total amount of memory.
Something like

size_t mp_task_heap_size = MIN(heap_caps_get_largest_free_block(MALLOC_CAP_8BIT),
                                          heap_caps_get_total_size(MALLOC_CAP_8BIT) / 3);

It does not change allocation on ESP32. On ESP32-S2 it allocates 71872 for python/109464 free for malloc, it's enough for WebREPL and upip.install('logging') works too. idf_heap_info() shows minimal seen size 25868, so we have some margin.
Or use some other percentage of the total size?
What do you think?