From G070 datasheets the first chapter mentions about the two low power timers. See first attachment. But that's all there is about them. Whether that's not correct?
That may be a copy-paste from another datasheet, but clearly there's no mention of them in the rest of the datasheet. Similarly, there's no mention of a LPUART, while you see one on the architecture image you posted.
In the STM32G0 power control ppt there is also picture which describes what features are available and what features not in STOP mode (see picture #2). There timers are gray and LPTIM1 & 2 are available.
Document: https://www.st.com/resource/en/product_training/STM32G0-System-Power-control-PWR.pdf
If I understand this configuration correctly standard timers like TIM6 & 7 in my case are clock source HSI and it shouldn't be running on STOP1 mode (see picture #3)?
Well, judging from the clock distribution diagram, all timers are clocked via SYSCLK (and then prescalers), which itself can be any of the clock sources, including LSE and LSI.
But if you have selected HSI for SYSCLK, it should be HSI. Right.
(Note that the datasheets for the STM32 are only giving a very high-level view of everything. You need to also refer to the reference manuals to get more detailed information (ref. RM0454)
I haven't found any mention of the LPTIM timers in there either, so I doubt they actually exist on this series.)
My guess now with your description is that one of the 2 timers may have generated a pending interrupt flag *before* you enter the Stop mode, and then, if the corresponding interrupts are not disabled, the MCU will wake up immediately - not from interrupts that would have been generated when the MCU is in Stop mode, but just before entering it. It could help to have a look at the IRQ handler functions you have written for both timers. To further test it, you could try clearing the interrupt flags of both timers just before calling HAL_PWR_EnterSTOPMode() instead of disabling the 2 interrupts, and see if it still wakes up.
Once you made sure there can't be any pending interrupt from these timers before entering Stop mode, one other thing to consider is the following:
"Some peripherals with wakeup capability can enable the HSI16 RC during Stop mode,
so as to get clock for processing the wakeup event. "
Check that you haven't configured some peripheral with such a capability. (I think that can be the USART for instance.) For this case, what you can test is set the clock to HSE instead (hoping you have an external crystal) - if the MCU doesn't wake up anymore while the timers interrupts are still enabled, then it may be due to this last point.