When monitoring network traffic with a protocol analyser, I’ve not noted unexpected DHCP traffic being generated by the iPad - a DHCP handshake typically only occurs when either joining a network, or upon expiry of the DHCP lease.
Given that a DHCP handshake will occur when (re)joining a WiFi network, perhaps your network is sending 802.11 de-authorisation/disassociate frames (to your iPad) if a duplicate MAC Address is detected on both wired and wireless network segments? This behaviour would be designed to inhibit and mitigate network Spanning Tree and Routing issues when a client device is simultaneously connected to two network segments.
https://en.wikipedia.org/wiki/Spanning_Tree_Protocol
If your wired and wireless network segments are part of the same network subnet (as you will often find in domestic environments - but would be very unusual on corporate/enterprise networks) Spanning Tree and Routing issues would not require mitigation.
The iPad network interface is not designed to be dual-homed. The iPad is primarily designed to be used in a WiFi-enabled environment. Whilst ethernet adapters are available for iPad, they would typically be used where WiFi is not available - or where a wired connection is needed for operational reasons. In the latter case, WiFi is assumed to be either unavailable or disabled.
iPad does employ rudimentary connection management - in that its automatic connection to WiFi networks can be enabled or disabled. However, iPad network connections cannot be natively prioritised.
Some third-party Apps for iOS/iPadOS are available that augment native network functionality by installing a local proxy service (this typically being utilised with VPN and/or secure DNS services such as DNSSEC, DoH and DoT - and for implementing connection and traffic filtering rulesets). I’m not personally aware of any third-party Apps that provide network prioritisation, bit you might conduct to research into this yourself.
Given that this analysis is based upon limited information, in isolation from your network and analysis tools, it should be relatively easy to prove the provided hypotheses by connecting to only WiFi (i.e, without a wired ethernet connection) or by locally disabling WiFi when connected to your network via an ethernet adapter. If network connectivity stabilises - and unexpected DHCP traffic is eliminated, you will have identified the cause.
I hope this somewhat simplified explanation provides some insight into what may be occurring on your network - and the behaviours observed.
